Converse, Inverse and Contrapositive Statements
Inverse Statement: The inverse of a conditional statement is formed by negating both the hypothesis and the conclusion of the original statement.
Contrapositive Statement: The contrapositive of a conditional statement is formed by switching the hypothesis and conclusion of the original statement and negating both.
| Statement | Converse | Inverse | Contrapositive |
|---|---|---|---|
| If p, then q | If q, then p | If not p, then not q | If not q, then not p |
Example of Inverse Statements
Original Statement: If a number is even, then it is divisible by 2.
Inverse Statement: If a number is not even, then it is not divisible by 2.
Original Statement: If x > 5, then 2x > 10.
Inverse Statement: If x ≤ 5, then 2x ≤ 10.
Example of Contrapositive Statements
Original Statement: If a shape is a square, then it has four equal sides.
Contrapositive Statement: If a shape does not have four equal sides, then it is not a square.
Original Statement: If a number is even, then it is divisible by 2.
Contrapositive: If a number is not divisible by 2, then it is not even.
Converse Statement
Converse Statement is a type of conditional statement where the hypothesis (or antecedent) and conclusion (or consequence) are reversed relative to a given conditional statement.
For instance, consider the statement: “If a triangle ABC is an equilateral triangle, then all its interior angles are equal.” The converse of this statement would be: “If all the interior angles of triangle ABC are equal, then it is an equilateral triangle”
In this article, we will discuss all the things related to the Converse statement in detail.
Table of Content
- What is a Converse Statement?
- How to Write a Converse Statement?
- Examples of Converse Statements
- Truth Value of a Converse Statement
- Truth Table for Converse Statement
- Other Types of Statements