# Inverse of a Conditional Statement

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

## How to Find

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

To find the inverse,

negate both *p* and *q*.

Conditional statement: hypothesis and conclusion

## Example 1

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

So ~*p* → ~*q*:

If 2 is **not** a prime number (~*p*),

then 2 is **not** an odd number (~*q*).

## Example 2

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

So ~*p* → ~*q*:

If he **is** in his room,

then he is **not** playing basketball.

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