# Contrapositive of a Conditional Statement

How to find the contrapositive of a conditional statement: examples and their solutions.

## How to Find

The contrapositive of a *p* → *q* is ~*q* → ~*p*.

To find the contrapositive,

negate and switch both *p* and *q*.

Conditional statement: hypothesis and conclusion

## Example 1

*p*: 2 is a prime number.*q*: 2 is an odd number.

So ~*q* → ~*p*:

If 2 is **not** an odd number (~*q*),

then 2 is **not** a prime number (~*p*).

## Example 2

*p*: He is not in his room.*q*: He is playing basketball.

So ~*q* → ~*p*:

If he is **not** playing basketball,

then he **is** in his room.

About ~*p*:*p* has **not**.

Then ~*p* will have two **not**-s.

So just remove the first **not**.

It's like -(-1) = +1.

Statement, negation