hypothesis and conclusion in statement

The Scientific Method by Science Made Simple

Understanding and using the scientific method.

The Scientific Method is a process used to design and perform experiments. It's important to minimize experimental errors and bias, and increase confidence in the accuracy of your results.

In the previous sections, we talked about how to pick a good topic and specific question to investigate. Now we will discuss how to carry out your investigation.

Steps of the Scientific Method

• Observation/Research
• Experimentation

Now that you have settled on the question you want to ask, it's time to use the Scientific Method to design an experiment to answer that question.

If your experiment isn't designed well, you may not get the correct answer. You may not even get any definitive answer at all!

The Scientific Method is a logical and rational order of steps by which scientists come to conclusions about the world around them. The Scientific Method helps to organize thoughts and procedures so that scientists can be confident in the answers they find.

OBSERVATION is first step, so that you know how you want to go about your research.

HYPOTHESIS is the answer you think you'll find.

PREDICTION is your specific belief about the scientific idea: If my hypothesis is true, then I predict we will discover this.

EXPERIMENT is the tool that you invent to answer the question, and

CONCLUSION is the answer that the experiment gives.

Don't worry, it isn't that complicated. Let's take a closer look at each one of these steps. Then you can understand the tools scientists use for their science experiments, and use them for your own.

OBSERVATION

This step could also be called "research." It is the first stage in understanding the problem.

After you decide on topic, and narrow it down to a specific question, you will need to research everything that you can find about it. You can collect information from your own experiences, books, the internet, or even smaller "unofficial" experiments.

Let's continue the example of a science fair idea about tomatoes in the garden. You like to garden, and notice that some tomatoes are bigger than others and wonder why.

Because of this personal experience and an interest in the problem, you decide to learn more about what makes plants grow.

For this stage of the Scientific Method, it's important to use as many sources as you can find. The more information you have on your science fair topic, the better the design of your experiment is going to be, and the better your science fair project is going to be overall.

Also try to get information from your teachers or librarians, or professionals who know something about your science fair project. They can help to guide you to a solid experimental setup.

The next stage of the Scientific Method is known as the "hypothesis." This word basically means "a possible solution to a problem, based on knowledge and research."

The hypothesis is a simple statement that defines what you think the outcome of your experiment will be.

All of the first stage of the Scientific Method -- the observation, or research stage -- is designed to help you express a problem in a single question ("Does the amount of sunlight in a garden affect tomato size?") and propose an answer to the question based on what you know. The experiment that you will design is done to test the hypothesis.

Using the example of the tomato experiment, here is an example of a hypothesis:

TOPIC: "Does the amount of sunlight a tomato plant receives affect the size of the tomatoes?"

HYPOTHESIS: "I believe that the more sunlight a tomato plant receives, the larger the tomatoes will grow.

This hypothesis is based on:

(1) Tomato plants need sunshine to make food through photosynthesis, and logically, more sun means more food, and;

(2) Through informal, exploratory observations of plants in a garden, those with more sunlight appear to grow bigger.

The hypothesis is your general statement of how you think the scientific phenomenon in question works.

Your prediction lets you get specific -- how will you demonstrate that your hypothesis is true? The experiment that you will design is done to test the prediction.

An important thing to remember during this stage of the scientific method is that once you develop a hypothesis and a prediction, you shouldn't change it, even if the results of your experiment show that you were wrong.

An incorrect prediction does NOT mean that you "failed." It just means that the experiment brought some new facts to light that maybe you hadn't thought about before.

Continuing our tomato plant example, a good prediction would be: Increasing the amount of sunlight tomato plants in my experiment receive will cause an increase in their size compared to identical plants that received the same care but less light.

This is the part of the scientific method that tests your hypothesis. An experiment is a tool that you design to find out if your ideas about your topic are right or wrong.

It is absolutely necessary to design a science fair experiment that will accurately test your hypothesis. The experiment is the most important part of the scientific method. It's the logical process that lets scientists learn about the world.

On the next page, we'll discuss the ways that you can go about designing a science fair experiment idea.

The final step in the scientific method is the conclusion. This is a summary of the experiment's results, and how those results match up to your hypothesis.

You have two options for your conclusions: based on your results, either:

(1) YOU CAN REJECT the hypothesis, or

(2) YOU CAN NOT REJECT the hypothesis.

This is an important point!

You can not PROVE the hypothesis with a single experiment, because there is a chance that you made an error somewhere along the way.

What you can say is that your results SUPPORT the original hypothesis.

If your original hypothesis didn't match up with the final results of your experiment, don't change the hypothesis.

Instead, try to explain what might have been wrong with your original hypothesis. What information were you missing when you made your prediction? What are the possible reasons the hypothesis and experimental results didn't match up?

Remember, a science fair experiment isn't a failure simply because does not agree with your hypothesis. No one will take points off if your prediction wasn't accurate. Many important scientific discoveries were made as a result of experiments gone wrong!

A science fair experiment is only a failure if its design is flawed. A flawed experiment is one that (1) doesn't keep its variables under control, and (2) doesn't sufficiently answer the question that you asked of it.

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Home » What is a Hypothesis – Types, Examples and Writing Guide

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

• Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
• Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
• Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
• Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
• Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
• Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

• Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
• Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
• Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
• Education : “Implementing a new teaching method will result in higher student achievement scores.”
• Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
• Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
• Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

When to use Hypothesis

Here are some common situations in which hypotheses are used:

• In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
• In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
• I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

• Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
• Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
• Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
• Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
• Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
• Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
• Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

• Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
• Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
• Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
• Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
• Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
• Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

• Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
• May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
• May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
• Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
• Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
• May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

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Muhammad Hassan

Researcher, Academic Writer, Web developer

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Conditional Statement – Definition, Truth Table, Examples, FAQs

What is a conditional statement, how to write a conditional statement, what is a biconditional statement, solved examples on conditional statements, practice problems on conditional statements, frequently asked questions about conditional statements.

A conditional statement is a statement that is written in the “If p, then q” format. Here, the statement p is called the hypothesis and q is called the conclusion. It is a fundamental concept in logic and mathematics. 

Conditional statement symbol :  p → q

A conditional statement consists of two parts.

• The “if” clause, which presents a condition or hypothesis.
• The “then” clause, which indicates the consequence or result that follows if the condition is true. 

Example : If you brush your teeth, then you won’t get cavities.

Hypothesis (Condition): If you brush your teeth

Conclusion (Consequence): then you won’t get cavities 

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Conditional Statement: Definition

A conditional statement is characterized by the presence of “if” as an antecedent and “then” as a consequent. A conditional statement, also known as an “if-then” statement consists of two parts:

• The “if” clause (hypothesis): This part presents a condition, situation, or assertion. It is the initial condition that is being considered.
• The “then” clause (conclusion): This part indicates the consequence, result, or action that will occur if the condition presented in the “if” clause is true or satisfied. 

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Representation of Conditional Statement

The conditional statement of the form ‘If p, then q” is represented as p → q. 

It is pronounced as “p implies q.”

Different ways to express a conditional statement are:

• p implies q
• p is sufficient for q
• q is necessary for p

Parts of a Conditional Statement

There are two parts of conditional statements, hypothesis and conclusion. The hypothesis or condition will begin with the “if” part, and the conclusion or action will begin with the “then” part. A conditional statement is also called “implication.”

Conditional Statements Examples:

Example 1: If it is Sunday, then you can go to play. 

Hypothesis: If it is Sunday

Conclusion: then you can go to play. 

Example 2: If you eat all vegetables, then you can have the dessert.

Condition: If you eat all vegetables

Conclusion: then you can have the dessert 

To form a conditional statement, follow these concise steps:

Step 1 : Identify the condition (antecedent or “if” part) and the consequence (consequent or “then” part) of the statement.

Step 2 : Use the “if… then…” structure to connect the condition and consequence.

Step 3 : Ensure the statement expresses a logical relationship where the condition leads to the consequence.

Example 1 : “If you study (condition), then you will pass the exam (consequence).” 

This conditional statement asserts that studying leads to passing the exam. If you study (condition is true), then you will pass the exam (consequence is also true).

Example 2 : If you arrange the numbers from smallest to largest, then you will have an ascending order.

Hypothesis: If you arrange the numbers from smallest to largest

Conclusion: then you will have an ascending order

Truth Table for Conditional Statement

The truth table for a conditional statement is a table used in logic to explore the relationship between the truth values of two statements. It lists all possible combinations of truth values for “p” and “q” and determines whether the conditional statement is true or false for each combination. 

The truth value of p → q is false only when p is true and q is False. 

If the condition is false, the consequence doesn’t affect the truth of the conditional; it’s always true.

In all the other cases, it is true.

The truth table is helpful in the analysis of possible combinations of truth values for hypothesis or condition and conclusion or action. It is useful to understand the presence of truth or false statements. 

Converse, Inverse, and Contrapositive

The converse, inverse, and contrapositive are three related conditional statements that are derived from an original conditional statement “p → q.” 

Consider a conditional statement: If I run, then I feel great.

• Converse: 

The converse of “p → q” is “q → p.” It reverses the order of the original statement. While the original statement says “if p, then q,” the converse says “if q, then p.” 

Converse: If I feel great, then I run.

• Inverse: 

The inverse of “p → q” is “~p → ~q,” where “” denotes negation (opposite). It negates both the antecedent (p) and the consequent (q). So, if the original statement says “if p, then q,” the inverse says “if not p, then not q.”

Inverse : If I don’t run, then I don’t feel great.

• Contrapositive: 

The contrapositive of “p → q” is “~q → ~p.” It reverses the order and also negates both the statements. So, if the original statement says “if p, then q,” the contrapositive says “if not q, then not p.”

Contrapositive: If I don’t feel great, then I don’t run.

A biconditional statement is a type of compound statement in logic that expresses a bidirectional or two-way relationship between two statements. It asserts that “p” is true if and only if “q” is true, and vice versa. In symbolic notation, a biconditional statement is represented as “p ⟺ q.”

In simpler terms, a biconditional statement means that the truth of “p” and “q” are interdependent. 

If “p” is true, then “q” must also be true, and if “q” is true, then “p” must be true. Conversely, if “p” is false, then “q” must be false, and if “q” is false, then “p” must be false. 

Biconditional statements are often used to express equality, equivalence, or conditions where two statements are mutually dependent for their truth values. 

Examples : 

• I will stop my bike if and only if the traffic light is red.  
• I will stay if and only if you play my favorite song.

Facts about Conditional Statements

• The negation of a conditional statement “p → q” is expressed as “p and not q.” It is denoted as “𝑝 ∧ ∼𝑞.” 
• The conditional statement is not logically equivalent to its converse and inverse.
• The conditional statement is logically equivalent to its contrapositive. 
• Thus, we can write p → q ∼q → ∼p

In this article, we learned about the fundamentals of conditional statements in mathematical logic, including their structure, parts, truth tables, conditional logic examples, and various related concepts. Understanding conditional statements is key to logical reasoning and problem-solving. Now, let’s solve a few examples and practice MCQs for better comprehension.

Example 1: Identify the hypothesis and conclusion. 

If you sing, then I will dance.

Solution : 

Given statement: If you sing, then I will dance.

Here, the antecedent or the hypothesis is “if you sing.”

The conclusion is “then I will dance.”

Example 2: State the converse of the statement: “If the switch is off, then the machine won’t work.” 

Here, p: The switch is off

q: The machine won’t work.

The conditional statement can be denoted as p → q.

Converse of p → q is written by reversing the order of p and q in the original statement.

Converse of  p → q is q → p.

Converse of  p → q: q → p: If the machine won’t work, then the switch is off.

Example 3: What is the truth value of the given conditional statement? 

If 2+2=5 , then pigs can fly.

Solution:  

q: Pigs can fly.

The statement p is false. Now regardless of the truth value of statement q, the overall statement will be true. 

F → F = T

Hence, the truth value of the statement is true. 

Conditional Statement - Definition, Truth Table, Examples, FAQs

Attend this quiz & Test your knowledge.

What is the antecedent in the given conditional statement? If it’s sunny, then I’ll go to the beach.

A conditional statement can be expressed as, what is the converse of “a → b”, when the antecedent is true and the consequent is false, the conditional statement is.

What is the meaning of conditional statements?

Conditional statements, also known as “if-then” statements, express a cause-and-effect or logical relationship between two propositions.

When does the truth value of a conditional statement is F?

A conditional statement is considered false when the antecedent is true and the consequent is false.

What is the contrapositive of a conditional statement?

The contrapositive reverses the order of the statements and also negates both the statements. It is equivalent in truth value to the original statement.

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15 Hypothesis Examples

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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A hypothesis is defined as a testable prediction , and is used primarily in scientific experiments as a potential or predicted outcome that scientists attempt to prove or disprove (Atkinson et al., 2021; Tan, 2022).

In my types of hypothesis article, I outlined 13 different hypotheses, including the directional hypothesis (which makes a prediction about an effect of a treatment will be positive or negative) and the associative hypothesis (which makes a prediction about the association between two variables).

This article will dive into some interesting examples of hypotheses and examine potential ways you might test each one.

Hypothesis Examples

1. “inadequate sleep decreases memory retention”.

Field: Psychology

Type: Causal Hypothesis A causal hypothesis explores the effect of one variable on another. This example posits that a lack of adequate sleep causes decreased memory retention. In other words, if you are not getting enough sleep, your ability to remember and recall information may suffer.

How to Test:

To test this hypothesis, you might devise an experiment whereby your participants are divided into two groups: one receives an average of 8 hours of sleep per night for a week, while the other gets less than the recommended sleep amount.

During this time, all participants would daily study and recall new, specific information. You’d then measure memory retention of this information for both groups using standard memory tests and compare the results.

Should the group with less sleep have statistically significant poorer memory scores, the hypothesis would be supported.

Ensuring the integrity of the experiment requires taking into account factors such as individual health differences, stress levels, and daily nutrition.

Relevant Study: Sleep loss, learning capacity and academic performance (Curcio, Ferrara & De Gennaro, 2006)

2. “Increase in Temperature Leads to Increase in Kinetic Energy”

Field: Physics

Type: Deductive Hypothesis The deductive hypothesis applies the logic of deductive reasoning – it moves from a general premise to a more specific conclusion. This specific hypothesis assumes that as temperature increases, the kinetic energy of particles also increases – that is, when you heat something up, its particles move around more rapidly.

This hypothesis could be examined by heating a gas in a controlled environment and capturing the movement of its particles as a function of temperature.

You’d gradually increase the temperature and measure the kinetic energy of the gas particles with each increment. If the kinetic energy consistently rises with the temperature, your hypothesis gets supporting evidence.

Variables such as pressure and volume of the gas would need to be held constant to ensure validity of results.

3. “Children Raised in Bilingual Homes Develop Better Cognitive Skills”

Field: Psychology/Linguistics

Type: Comparative Hypothesis The comparative hypothesis posits a difference between two or more groups based on certain variables. In this context, you might propose that children raised in bilingual homes have superior cognitive skills compared to those raised in monolingual homes.

Testing this hypothesis could involve identifying two groups of children: those raised in bilingual homes, and those raised in monolingual homes.

Cognitive skills in both groups would be evaluated using a standard cognitive ability test at different stages of development. The examination would be repeated over a significant time period for consistency.

If the group raised in bilingual homes persistently scores higher than the other, the hypothesis would thereby be supported.

The challenge for the researcher would be controlling for other variables that could impact cognitive development, such as socio-economic status, education level of parents, and parenting styles.

Relevant Study: The cognitive benefits of being bilingual (Marian & Shook, 2012)

4. “High-Fiber Diet Leads to Lower Incidences of Cardiovascular Diseases”

Field: Medicine/Nutrition

Type: Alternative Hypothesis The alternative hypothesis suggests an alternative to a null hypothesis. In this context, the implied null hypothesis could be that diet has no effect on cardiovascular health, which the alternative hypothesis contradicts by suggesting that a high-fiber diet leads to fewer instances of cardiovascular diseases.

To test this hypothesis, a longitudinal study could be conducted on two groups of participants; one adheres to a high-fiber diet, while the other follows a diet low in fiber.

After a fixed period, the cardiovascular health of participants in both groups could be analyzed and compared. If the group following a high-fiber diet has a lower number of recorded cases of cardiovascular diseases, it would provide evidence supporting the hypothesis.

Control measures should be implemented to exclude the influence of other lifestyle and genetic factors that contribute to cardiovascular health.

Relevant Study: Dietary fiber, inflammation, and cardiovascular disease (King, 2005)

5. “Gravity Influences the Directional Growth of Plants”

Field: Agronomy / Botany

Type: Explanatory Hypothesis An explanatory hypothesis attempts to explain a phenomenon. In this case, the hypothesis proposes that gravity affects how plants direct their growth – both above-ground (toward sunlight) and below-ground (towards water and other resources).

The testing could be conducted by growing plants in a rotating cylinder to create artificial gravity.

Observations on the direction of growth, over a specified period, can provide insights into the influencing factors. If plants consistently direct their growth in a manner that indicates the influence of gravitational pull, the hypothesis is substantiated.

It is crucial to ensure that other growth-influencing factors, such as light and water, are uniformly distributed so that only gravity influences the directional growth.

6. “The Implementation of Gamified Learning Improves Students’ Motivation”

Field: Education

Type: Relational Hypothesis The relational hypothesis describes the relation between two variables. Here, the hypothesis is that the implementation of gamified learning has a positive effect on the motivation of students.

To validate this proposition, two sets of classes could be compared: one that implements a learning approach with game-based elements, and another that follows a traditional learning approach.

The students’ motivation levels could be gauged by monitoring their engagement, performance, and feedback over a considerable timeframe.

If the students engaged in the gamified learning context present higher levels of motivation and achievement, the hypothesis would be supported.

Control measures ought to be put into place to account for individual differences, including prior knowledge and attitudes towards learning.

Relevant Study: Does educational gamification improve students’ motivation? (Chapman & Rich, 2018)

7. “Mathematics Anxiety Negatively Affects Performance”

Field: Educational Psychology

Type: Research Hypothesis The research hypothesis involves making a prediction that will be tested. In this case, the hypothesis proposes that a student’s anxiety about math can negatively influence their performance in math-related tasks.

To assess this hypothesis, researchers must first measure the mathematics anxiety levels of a sample of students using a validated instrument, such as the Mathematics Anxiety Rating Scale.

Then, the students’ performance in mathematics would be evaluated through standard testing. If there’s a negative correlation between the levels of math anxiety and math performance (meaning as anxiety increases, performance decreases), the hypothesis would be supported.

It would be crucial to control for relevant factors such as overall academic performance and previous mathematical achievement.

8. “Disruption of Natural Sleep Cycle Impairs Worker Productivity”

Field: Organizational Psychology

Type: Operational Hypothesis The operational hypothesis involves defining the variables in measurable terms. In this example, the hypothesis posits that disrupting the natural sleep cycle, for instance through shift work or irregular working hours, can lessen productivity among workers.

To test this hypothesis, you could collect data from workers who maintain regular working hours and those with irregular schedules.

Measuring productivity could involve examining the worker’s ability to complete tasks, the quality of their work, and their efficiency.

If workers with interrupted sleep cycles demonstrate lower productivity compared to those with regular sleep patterns, it would lend support to the hypothesis.

Consideration should be given to potential confounding variables such as job type, worker age, and overall health.

9. “Regular Physical Activity Reduces the Risk of Depression”

Field: Health Psychology

Type: Predictive Hypothesis A predictive hypothesis involves making a prediction about the outcome of a study based on the observed relationship between variables. In this case, it is hypothesized that individuals who engage in regular physical activity are less likely to suffer from depression.

Longitudinal studies would suit to test this hypothesis, tracking participants’ levels of physical activity and their mental health status over time.

The level of physical activity could be self-reported or monitored, while mental health status could be assessed using standard diagnostic tools or surveys.

If data analysis shows that participants maintaining regular physical activity have a lower incidence of depression, this would endorse the hypothesis.

However, care should be taken to control other lifestyle and behavioral factors that could intervene with the results.

Relevant Study: Regular physical exercise and its association with depression (Kim, 2022)

10. “Regular Meditation Enhances Emotional Stability”

Type: Empirical Hypothesis In the empirical hypothesis, predictions are based on amassed empirical evidence . This particular hypothesis theorizes that frequent meditation leads to improved emotional stability, resonating with numerous studies linking meditation to a variety of psychological benefits.

Earlier studies reported some correlations, but to test this hypothesis directly, you’d organize an experiment where one group meditates regularly over a set period while a control group doesn’t.

Both groups’ emotional stability levels would be measured at the start and end of the experiment using a validated emotional stability assessment.

If regular meditators display noticeable improvements in emotional stability compared to the control group, the hypothesis gains credit.

You’d have to ensure a similar emotional baseline for all participants at the start to avoid skewed results.

11. “Children Exposed to Reading at an Early Age Show Superior Academic Progress”

Type: Directional Hypothesis The directional hypothesis predicts the direction of an expected relationship between variables. Here, the hypothesis anticipates that early exposure to reading positively affects a child’s academic advancement.

A longitudinal study tracking children’s reading habits from an early age and their consequent academic performance could validate this hypothesis.

Parents could report their children’s exposure to reading at home, while standardized school exam results would provide a measure of academic achievement.

If the children exposed to early reading consistently perform better acadically, it gives weight to the hypothesis.

However, it would be important to control for variables that might impact academic performance, such as socioeconomic background, parental education level, and school quality.

12. “Adopting Energy-efficient Technologies Reduces Carbon Footprint of Industries”

Field: Environmental Science

Type: Descriptive Hypothesis A descriptive hypothesis predicts the existence of an association or pattern related to variables. In this scenario, the hypothesis suggests that industries adopting energy-efficient technologies will resultantly show a reduced carbon footprint.

Global industries making use of energy-efficient technologies could track their carbon emissions over time. At the same time, others not implementing such technologies continue their regular tracking.

After a defined time, the carbon emission data of both groups could be compared. If industries that adopted energy-efficient technologies demonstrate a notable reduction in their carbon footprints, the hypothesis would hold strong.

In the experiment, you would exclude variations brought by factors such as industry type, size, and location.

13. “Reduced Screen Time Improves Sleep Quality”

Type: Simple Hypothesis The simple hypothesis is a prediction about the relationship between two variables, excluding any other variables from consideration. This example posits that by reducing time spent on devices like smartphones and computers, an individual should experience improved sleep quality.

A sample group would need to reduce their daily screen time for a pre-determined period. Sleep quality before and after the reduction could be measured using self-report sleep diaries and objective measures like actigraphy, monitoring movement and wakefulness during sleep.

If the data shows that sleep quality improved post the screen time reduction, the hypothesis would be validated.

Other aspects affecting sleep quality, like caffeine intake, should be controlled during the experiment.

Relevant Study: Screen time use impacts low‐income preschool children’s sleep quality, tiredness, and ability to fall asleep (Waller et al., 2021)

14. Engaging in Brain-Training Games Improves Cognitive Functioning in Elderly

Field: Gerontology

Type: Inductive Hypothesis Inductive hypotheses are based on observations leading to broader generalizations and theories. In this context, the hypothesis deduces from observed instances that engaging in brain-training games can help improve cognitive functioning in the elderly.

A longitudinal study could be conducted where an experimental group of elderly people partakes in regular brain-training games.

Their cognitive functioning could be assessed at the start of the study and at regular intervals using standard neuropsychological tests.

If the group engaging in brain-training games shows better cognitive functioning scores over time compared to a control group not playing these games, the hypothesis would be supported.

15. Farming Practices Influence Soil Erosion Rates

Type: Null Hypothesis A null hypothesis is a negative statement assuming no relationship or difference between variables. The hypothesis in this context asserts there’s no effect of different farming practices on the rates of soil erosion.

Comparing soil erosion rates in areas with different farming practices over a considerable timeframe could help test this hypothesis.

If, statistically, the farming practices do not lead to differences in soil erosion rates, the null hypothesis is accepted.

However, if marked variation appears, the null hypothesis is rejected, meaning farming practices do influence soil erosion rates. It would be crucial to control for external factors like weather, soil type, and natural vegetation.

The variety of hypotheses mentioned above underscores the diversity of research constructs inherent in different fields, each with its unique purpose and way of testing.

While researchers may develop hypotheses primarily as tools to define and narrow the focus of the study, these hypotheses also serve as valuable guiding forces for the data collection and analysis procedures, making the research process more efficient and direction-focused.

Hypotheses serve as a compass for any form of academic research. The diverse examples provided, from Psychology to Educational Studies, Environmental Science to Gerontology, clearly demonstrate how certain hypotheses suit specific fields more aptly than others.

It is important to underline that although these varied hypotheses differ in their structure and methods of testing, each endorses the fundamental value of empiricism in research. Evidence-based decision making remains at the heart of scholarly inquiry, regardless of the research field, thus aligning all hypotheses to the core purpose of scientific investigation.

Testing hypotheses is an essential part of the scientific method . By doing so, researchers can either confirm their predictions, giving further validity to an existing theory, or they might uncover new insights that could potentially shift the field’s understanding of a particular phenomenon. In either case, hypotheses serve as the stepping stones for scientific exploration and discovery.

Atkinson, P., Delamont, S., Cernat, A., Sakshaug, J. W., & Williams, R. A. (2021).  SAGE research methods foundations . SAGE Publications Ltd.

Curcio, G., Ferrara, M., & De Gennaro, L. (2006). Sleep loss, learning capacity and academic performance.  Sleep medicine reviews ,  10 (5), 323-337.

Kim, J. H. (2022). Regular physical exercise and its association with depression: A population-based study short title: Exercise and depression.  Psychiatry Research ,  309 , 114406.

King, D. E. (2005). Dietary fiber, inflammation, and cardiovascular disease.  Molecular nutrition & food research ,  49 (6), 594-600.

Marian, V., & Shook, A. (2012, September). The cognitive benefits of being bilingual. In Cerebrum: the Dana forum on brain science (Vol. 2012). Dana Foundation.

Tan, W. C. K. (2022). Research Methods: A Practical Guide For Students And Researchers (Second Edition) . World Scientific Publishing Company.

Waller, N. A., Zhang, N., Cocci, A. H., D’Agostino, C., Wesolek‐Greenson, S., Wheelock, K., … & Resnicow, K. (2021). Screen time use impacts low‐income preschool children’s sleep quality, tiredness, and ability to fall asleep. Child: care, health and development, 47 (5), 618-626.

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Biconditional Statement — Definition, Examples & How To Write

What is a biconditional statement?

A biconditional statement combines a conditional statement with its converse statement. Both the conditional and converse statements must be true to produce a biconditional statement.

If we remove the  if-then  part of a true conditional statement, combine the hypothesis and conclusion, and tuck in a phrase "if and only if," we can create  biconditional statements .

Geometry and logic cross paths many ways. One example is a  biconditional statement . To understand biconditional statements, we first need to review conditional and converse statements. Then we will see how these logic tools apply to geometry.

Conditional statements

In logic, concepts can be conditional, using an  if-then  statement:

If I have a pet goat, then my homework will be eaten.

If I have a triangle, then my polygon has only three sides.

If the polygon has only four sides, then the polygon is a quadrilateral.

If I eat lunch, then my mood will improve.

If I ask more questions in class, then I will understand the mathematics better.

If the quadrilateral has four congruent sides and angles, then the quadrilateral is a square.

Each of these conditional statements has a  hypothesis  ("If …") and a  conclusion  (" …, then …").

These statements can be true or false. Whether the conditional statement is true or false does not matter (well, it will eventually), so long as the second part (the conclusion) relates to, and is dependent on, the first part (the hypothesis).

Converse statements

To create a  converse statement  for a given conditional statement, switch the hypothesis and the conclusion. You may "clean up" the two parts for grammar without affecting the logic.

Take the first conditional statement from above:

Hypothesis: If I have a pet goat …

Conclusion: … then my homework will be eaten.

Create the converse statement:

Hypothesis: If my homework is eaten …

Conclusion: Then I have a pet goat.

Converse: If my homework is eaten, then I have a pet goat.

This converse statement is not true, as you can conceive of something … or someone … else eating your homework: your dog, your little brother. Your homework being eaten does not  automatically  mean you have a goat.

Let's apply the same concept of switching conclusion and hypothesis to one of the conditional geometry statements:

Conditional: If I have a triangle, then my polygon has only three sides.

Converse: If my polygon has only three sides, then I have a triangle.

This converse is true; remember, though, neither the original conditional statement nor its converse have to be true to be valid, logical statements.

Converse statement examples

For, "If the polygon has only four sides, then the polygon is a quadrilateral," write the converse statement.

Converse:  If the polygon is a quadrilateral, then the polygon has only four sides.

Try this one, too: "If the quadrilateral has four congruent sides and angles, then the quadrilateral is a square."

Converse:  If the quadrilateral is a square, then the quadrilateral has four congruent sides and angles.

How to write a biconditional statement

The general form (for goats, geometry or lunch) is:

Hypothesis  if and only if  conclusion .

Because the statement is biconditional (conditional in both directions), we can also write it this way, which is the converse statement:

Conclusion  if and only if  hypothesis .

Notice we can create  two  biconditional statements. If conditional statements are one-way streets, biconditional statements are the two-way streets of logic.

Both the conditional and converse statements must be true to produce a biconditional statement.

Conditional: If I have a triangle, then my polygon has only three sides. (true)

Converse: If my polygon has only three sides, then I have a triangle. (true)

Since both statements are true, we can write two biconditional statements:

I have a triangle if and only if my polygon has only three sides. (true)

My polygon has only three sides if and only if I have a triangle. (true)

You can do this if and only if both conditional and converse statements have the same truth value. They could both be  false  and you could still write a true biconditional statement ("My pet goat draws polygons if and only if my pet goat buys art supplies online.").

Let's see how different truth values prevent logical biconditional statements, using our pet goat:

Conditional: If I have a pet goat, then my homework will be eaten. (true)

Converse: If my homework is eaten, then I have a pet goat. (not true)

We can attempt, but fail to write, logical biconditional statements, but they will not make sense:

I have a pet goat if and only if my homework is eaten. (not true)

My homework will be eaten if and only if I have a pet goat. (not true)

Biconditional statement symbols

You may recall that logic symbols can replace words in statements. So the conditional statement, "If I have a pet goat, then my homework gets eaten" can be replaced with a  p  for the hypothesis, a  q  for the conclusion, and a  → \to →  for the connector:

For biconditional statements, we use a double arrow, ⇔ \Leftrightarrow ⇔ , since the truth works in both directions:

Biconditional statement examples

We still have several conditional geometry statements and their converses from above.

Conditional: If the polygon has only four sides, then the polygon is a quadrilateral. (true)

Converse: If the polygon is a quadrilateral, then the polygon has only four sides. (true)

Conditional: If the quadrilateral has four congruent sides and angles, then the quadrilateral is a square. (true)

Converse: If the quadrilateral is a square, then the quadrilateral has four congruent sides and angles. (true)

Try your hand at these first, then check below. The biconditional statements for these two sets would be:

The polygon has only four sides if and only if the polygon is a quadrilateral.

The polygon is a quadrilateral if and only if the polygon has only four sides.

The quadrilateral has four congruent sides and angles if and only if the quadrilateral is a square.

The quadrilateral is a square if and only if the quadrilateral has four congruent sides and angles.

More examples

See if you can write the converse and biconditional statements for these. You can "clean up" the words for grammar.

Try doing it before peeking below!

If I eat lunch, then my mood will improve. (true)

If my mood improves, then I will eat lunch. (true)

Biconditional statements:

I will eat lunch if and only if my mood improves.

My mood will improve if and only if I eat lunch.

And now the other leftover:

If I ask more questions in class, then I will understand the mathematics better. (true)

If I understand the mathematics better, then I will ask more questions in class. (false)

You cannot write a biconditional statement for this leftover; the truth values are not the same.

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How to State the Conclusion about a Hypothesis Test

After you have completed the statistical analysis and decided to reject or fail to reject the Null hypothesis, you need to state your conclusion about the claim. To get the correct wording, you need to recall which hypothesis was the claim.

If the claim was the null, then your conclusion is about whether there was sufficient evidence to reject the claim. Remember, we can never prove the null to be true, but failing to reject it is the next best thing. So, it is not correct to say, “Accept the Null.”

If the claim is the alternative hypothesis, your conclusion can be whether there was sufficient evidence to support (prove) the alternative is true.

Use the following table to help you make a good conclusion.

The best way to state the conclusion is to include the significance level of the test and a bit about the claim itself.

For example, if the claim was the alternative that the mean score on a test was greater than 85, and your decision was to  Reject then Null , then you could conclude: “ At the 5% significance level, there is sufficient evidence to support the claim that the mean score on the test was greater than 85. ”

The reason you should include the significance level is that the decision, and thus the conclusion, could be different if the significance level was not 5%.

If you are curious why we say “Fail to Reject the Null” instead of “Accept the Null,” this short video might be of interest:  Here

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It is concluded that the null hypothesis Ho is not rejected proportion p is greater than 0.5, at the 0.05 significance

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Dr. Dawn Wright

Calcworkshop

Conditional Statement If Then's Defined in Geometry - 15+ Examples!

// Last Updated: January 21, 2020 - Watch Video //

In today’s geometry lesson , you’re going to learn all about conditional statements!

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

We’re going to walk through several examples to ensure you know what you’re doing.

In addition, this lesson will prepare you for deductive reasoning and two column proofs later on.

Here we go!

What are Conditional Statements?

To better understand deductive reasoning, we must first learn about conditional statements.

A conditional statement has two parts: hypothesis ( if ) and conclusion ( then ).

In fact, conditional statements are nothing more than “If-Then” statements!

Sometimes a picture helps form our hypothesis or conclusion. Therefore, we sometimes use Venn Diagrams to visually represent our findings and aid us in creating conditional statements.

But to verify statements are correct, we take a deeper look at our if-then statements. This is why we form the converse , inverse , and contrapositive of our conditional statements.

What is the Converse of a Statement?

Well, the converse is when we switch or interchange our hypothesis and conclusion.

Conditional Statement : “If today is Wednesday, then yesterday was Tuesday.”

Hypothesis : “If today is Wednesday” so our conclusion must follow “Then yesterday was Tuesday.”

So the converse is found by rearranging the hypothesis and conclusion, as Math Planet accurately states.

Converse : “If yesterday was Tuesday, then today is Wednesday.”

What is the Inverse of a Statement?

Now the inverse of an If-Then statement is found by negating (making negative) both the hypothesis and conclusion of the conditional statement.

So using our current conditional statement, “If today is Wednesday, then yesterday was Tuesday”.

Inverse : “If today is not Wednesday, then yesterday was not Tuesday.”

What is a Contrapositive?

And the contrapositive is formed by interchanging the hypothesis and conclusion and then negating both.

Contrapositive : “If yesterday was not Tuesday, then today is not Wednesday”

What is a Biconditional Statement?

A statement written in “if and only if” form combines a reversible statement and its true converse. In other words the conditional statement and converse are both true.

Continuing with our initial condition, “If today is Wednesday, then yesterday was Tuesday.”

Biconditional : “Today is Wednesday if and only if yesterday was Tuesday.”

Examples of Conditional Statements

In the video below we will look at several harder examples of how to form a proper statement, converse, inverse, and contrapositive. And here’s a big hint…

Whenever you see “con” that means you switch! It’s like being a con-artist!

Moreover, we will detail the process for coming up with reasons for our conclusions using known postulates. We will review the ten postulates that we have learned so far, and add a few more problems dealing with perpendicular lines, planes, and perpendicular bisectors.

After this lesson, we will be ready to tackle deductive reasoning head-on, and feel confident as we march onward toward learning two-column proofs!

Conditional Statements – Lesson & Examples (Video)

• Introduction to conditional statements
• 00:00:25 – What are conditional statements, converses, and biconditional statements? (Examples #1-2)
• 00:05:21 – Understanding venn diagrams (Examples #3-4)
• 00:11:07 – Supply the missing venn diagram and conditional statement for each question (Examples #5-8)
• Exclusive Content for Member’s Only
• 00:17:48 – Write the statement and converse then determine if they are reversible (Examples #9-12)
• 00:29:17 – Understanding the inverse, contrapositive, and symbol notation
• 00:35:33 – Write the statement, converse, inverse, contrapositive, and biconditional statements for each question (Examples #13-14)
• 00:45:40 – Using geometry postulates to verify statements (Example #15)
• 00:53:23 – What are perpendicular lines, perpendicular planes and the perpendicular bisector?
• 00:56:26 – Using the figure, determine if the statement is true or false (Example #16)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

Get access to all the courses and over 450 HD videos with your subscription

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Still wondering if CalcWorkshop is right for you? Take a Tour and find out how a membership can take the struggle out of learning math.

Conditional Statement

A conditional statement is a part of mathematical reasoning which is a critical skill that enables students to analyze a given hypothesis without any reference to a particular context or meaning. In layman words, when a scientific inquiry or statement is examined, the reasoning is not based on an individual's opinion. Derivations and proofs need a factual and scientific basis. 

Mathematical critical thinking and logical reasoning are important skills that are required to solve maths reasoning questions.

In this mini-lesson, we will explore the world of conditional statements. We will walk through the answers to the questions like what is meant by a conditional statement, what are the parts of a conditional statement, and how to create conditional statements along with solved examples and interactive questions.

Lesson Plan  

What is meant by a conditional statement.

A statement that is of the form "If p, then q" is a conditional statement. Here 'p' refers to 'hypothesis' and 'q' refers to 'conclusion'.

For example, "If Cliff is thirsty, then she drinks water."

This is a conditional statement. It is also called an implication.

'\(\rightarrow\)' is the symbol used to represent the relation between two statements. For example, A\(\rightarrow\)B. It is known as the logical connector. It can be read as A implies B. 

Here are two more conditional statement examples

Example 1: If a number is divisible by 4, then it is divisible by 2.

Example 2: If today is Monday, then yesterday was Sunday.

What Are the Parts of a Conditional Statement?

Hypothesis (if) and Conclusion (then) are the two main parts that form a conditional statement.

Let us consider the above-stated example to understand the parts of a conditional statement.

Conditional Statement : If today is Monday, then yesterday was Sunday.

Hypothesis : "If today is Monday."

Conclusion : "Then yesterday was Sunday."

On interchanging the form of statement the relationship gets changed.

To check whether the statement is true or false here, we have subsequent parts of a conditional statement. They are:

• Contrapositive

Biconditional Statement

Let us consider hypothesis as statement A and Conclusion as statement B.

Following are the observations made:

Converse of Statement

When hypothesis and conclusion are switched or interchanged, it is termed as converse statement . For example,

Conditional Statement : “If today is Monday, then yesterday was Sunday.”

Hypothesis : “If today is Monday”

Converse : “If yesterday was Sunday, then today is Monday.”

Here the conditional statement logic is, If B, then A (B → A)

Inverse of Statement

When both the hypothesis and conclusion of the conditional statement are negative, it is termed as an inverse of the statement. For example,

Conditional Statement: “If today is Monday, then yesterday was Sunday”.

Inverse : “If today is not Monday, then yesterday was not Sunday.”

Here the conditional statement logic is, If not A, then not B (~A → ~B)

Contrapositive Statement

When the hypothesis and conclusion are negative and simultaneously interchanged, then the statement is contrapositive. For example,

Contrapositive: “If yesterday was not Sunday, then today is not Monday”

Here the conditional statement logic is, if not B, then not A (~B → ~A)

The statement is a biconditional statement when a statement satisfies both the conditions as true, being conditional and converse at the same time. For example,

Biconditional : “Today is Monday if and only if yesterday was Sunday.”

Here the conditional statement logic is, A if and only if B (A ↔ B)

How to Create Conditional Statements?

Here, the point to be kept in mind is that the 'If' and 'then' part must be true.

If a number is a perfect square , then it is even.

• 'If' part is a number that is a perfect square.

Think of 4 which is a perfect square.

This has become true.

• The 'then' part is that the number should be even. 4 is even.

This has also become true. 

Thus, we have set up a conditional statement.

Let us hypothetically consider two statements, statement A and statement B. Observe the truth table for the statements:

According to the table, only if the hypothesis (A) is true and the conclusion (B) is false then, A → B will be false, or else A → B will be true for all other conditions.

• A sentence needs to be either true or false, but not both, to be considered as a mathematically accepted statement.
• Any sentence which is either imperative or interrogative or exclamatory cannot be considered a mathematically validated statement. 
• A sentence containing one or many variables is termed as an open statement. An open statement can become a statement if the variables present in the sentence are replaced by definite values.

Solved Examples

Let us have a look at a few solved examples on conditional statements.

Identify the types of conditional statements.

There are four types of conditional statements:

• If condition
• If-else condition
• Nested if-else
• If-else ladder.

Ray tells "If the perimeter of a rectangle is 14, then its area is 10."

Which of the following could be the counterexamples? Justify your decision.

a) A rectangle with sides measuring 2 and 5

b) A rectangle with sides measuring 10 and 1

c) A rectangle with sides measuring 1 and 5

d) A rectangle with sides measuring 4 and 3

a) Rectangle with sides 2 and 5: Perimeter = 14 and area = 10

Both 'if' and 'then' are true.

b) Rectangle with sides 10 and 1: Perimeter = 22 and area = 10

'If' is false and 'then' is true.

c) Rectangle with sides 1 and 5: Perimeter = 12 and area = 5

Both 'if' and 'then' are false.

d) Rectangle with sides 4 and 3: Perimeter = 14 and area = 12

'If' is true and 'then' is false.

Joe examined the set of numbers {16, 27, 24} to check if they are the multiples of 3. He claimed that they are divisible by 9. Do you agree or disagree? Justify your answer.

Conditional statement : If a number is a multiple of 3, then it is divisible by 9.

Let us find whether the conditions are true or false.

a) 16 is not a multiple of 3. Thus, the condition is false. 

16 is not divisible by 9. Thus, the conclusion is false. 

b) 27 is a multiple of 3. Thus, the condition is true.

27 is divisible by 9. Thus, the conclusion is true. 

c) 24 is a multiple of 3. Thus the condition is true.

24 is not divisible by 9. Thus the conclusion is false.

Write the converse, inverse, and contrapositive statement for the following conditional statement. 

If you study well, then you will pass the exam.

The given statement is - If you study well, then you will pass the exam.

It is of the form, "If p, then q"

The converse statement is, "You will pass the exam if you study well" (if q, then p).

The inverse statement is, "If you do not study well then you will not pass the exam" (if not p, then not q).

The contrapositive statement is, "If you did not pass the exam, then you did not study well" (if not q, then not p).

Interactive Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

Let's Summarize

The mini-lesson targeted the fascinating concept of the conditional statement. The math journey around conditional statements started with what a student already knew and went on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever.

About Cuemath

At  Cuemath , our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.

FAQs on Conditional Statement

1. what is the most common conditional statement.

'If and then' is the most commonly used conditional statement.

2. When do you use a conditional statement?

Conditional statements are used to justify the given condition or two statements as true or false.

3. What is if and if-else statement?

If is used when a specified condition is true. If-else is used when a particular specified condition is not satisfying and is false.

4. What is the symbol for a conditional statement?

'\(\rightarrow\)' is the symbol used to represent the relation between two statements. For example, A\(\rightarrow\)B. It is known as the logical connector. It can be read as A implies B.

5. What is the Contrapositive of a conditional statement?

If not B, then not A (~B → ~A)

6. What is a universal conditional statement?

Conditional statements are those statements where a hypothesis is followed by a conclusion. It is also known as an " If-then" statement. If the hypothesis is true and the conclusion is false, then the conditional statement is false. Likewise, if the hypothesis is false the whole statement is false. Conditional statements are also termed as implications.

Conditional Statement: If today is Monday, then yesterday was Sunday

Hypothesis: "If today is Monday."

Conclusion: "Then yesterday was Sunday."

If A, then B (A → B)

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What is the difference between a hypothesis and a conclusion?

And a conclusion is drawn AFTER the experiment is performed, and reports whether or not the results of the experiment supported the original hypothesis...

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Moldova, Presidential Election and Constitutional Referendum, 20 October 2024: Statement of Preliminary Findings and Conclusions