A statement that is of the form "If p then q" is a conditional statement. Here 'p' refers to 'hypotheses' and 'q' refers to 'conclusion'. Show
For example, "If Cliff is thirsty, then she drinks water." This is a conditional statement. It is also called an implication. The converse statement is " If Cliff drinks water then she is thirsty". A converse statement is the opposite of a conditional statement. It is to be noted that not always the converse of a conditional statement is true. For example, in geometry, "If a closed shape has four sides then it is a square" is a conditional statement, The truthfulness of a converse statement depends on the truth of hypotheses of the conditional statement. In this mini-lesson, we will learn about the converse statement, how inverse and contrapositive are obtained from a conditional statement, converse statement definition, converse statement geometry, and converse statement symbol. Lesson PlanWhat Is Converse Statement?A statement obtained by reversing the hypothesis and conclusion of a conditional statement is called a converse statement. ExplanationLet us understand the terms "hypothesis" and "conclusion." A statement which is of the form of "if p then q" is a conditional statement, where 'p' is called hypothesis and 'q' is called the conclusion. A converse statement is gotten by exchanging the positions of 'p' and 'q' in the given condition.
For example, "If Cliff is thirsty, then she drinks water" is a condition. The converse statement is "If Cliff drinks water, then she is thirsty." The hypothesis 'p' and conclusion 'q' interchange their places in a converse statement. What Is Inverse Statement?DefinitionA statement obtained by negating the hypothesis and conclusion of a conditional statement. ExplanationAn inverse statement changes the "if p then q" statement to the form of "if not p then not q."
For example, "If John has time, then he works out in the gym." The inverse statement is "If John does not have time, then he does not work out in the gym." What Is Contrapositive Statement?DefinitionA statement obtained by exchanging the hypothesis and conclusion of an inverse statement. ExplanationA contrapositive statement changes "if not p then not q" to "if not q to then, not p."
For example, If it is a holiday, then I will wake up late. - Conditional statement If it is not a holiday, then I will not wake up late. - Inverse statement If I am not waking up late, then it is not a holiday. - Contrapositive statement What Is a Conditional Statement?DefinitionA conditional statement is a statement in the form of "if p then q," where 'p' and 'q' are called a hypothesis and conclusion. A conditional statement defines that if the hypothesis is true then the conclusion is true. For example, "If we have to to travel for a long distance, then we have to take a taxi" is a conditional statement. Converse of a Conditional StatementTo get the converse of a conditional statement, interchange the places of hypothesis and conclusion.
For example, If you eat a lot of vegetables, then you will be healthy. - Conditional statement If you are healthy, then you eat a lot of vegetables. - Converse of Conditional statement Inverse of Conditional StatementTo get the inverse of a conditional statement, we negate both the hypothesis and conclusion.
For example, If you read books, then you will gain knowledge. - Conditional statement If you do not read books, then you will not gain knowledge. -Inverse of conditional statement Contrapositive of Conditional StatementTo get the contrapositive of a conditional statement, we negate the hypothesis and conclusion and exchange their position.
For example, Emily's dad watches a movie if he has time. - Conditional statement If Emily's dad does not have time, then he does not watch a movie. - Contrapositive of a conditional statement
Solved ExamplesWrite the converse, inverse, and contrapositive statement of the following conditional statement. If you win the race then you will get a prize. Solution The conditional statement given is "If you win the race then you will get a prize." It is of the form "If p then q". Here 'p' is the hypothesis and 'q' is the conclusion.
From the given inverse statement, write down its conditional and contrapositive statements. If there is no accomodation in the hotel, then we are not going on a vacation. Solution The inverse statement given is "If there is no accomodation in the hotel, then we are not going on a vacation." It is of the form "If not p then not q" Here 'p' is the hypothesis and 'q' is the conclusion.
Write the converse, inverse, and contrapositive statement for the following conditional statement. If you study well then you will pass the exam. Solution Given statement is - If you study well then you will pass the exam. It is of the form "If p then q".
Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result. The mini-lesson targeted the fascinating concept of converse statement. Hope you enjoyed learning! Now you can easily find the converse, inverse, and contrapositive of any conditional statement you are given! About CuemathAt 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. Frequently Asked Questions (FAQs)
A statement that conveys the opposite meaning of a statement is called its negation.
A statement formed by interchanging the hypothesis and conclusion of a statement is its converse. |