# Converse Statement

How to find the converse of a conditional statement: definition, 2 examples, and their solutions.

## Definition

### Definition

[q → p] is the converse

of the conditional statement [p → q].

To find the converse,

switch p and q.

## Example 1

### Example

### Solution

The structure of the given conditional is

[if ... , then ...].

So the statement behind if is p:

2 is a prime number.

And the statement behind then is q:

2 is an odd number.

The given conditional statement is p → q.

Then the converse is,

switch p and q,

q → p.

Write the converse q → p.

If, q, 2 is an odd number,

then, p, 2 is a prime number.

So the converse is

if 2 is an odd number,

then 2 is a prime number.

## Example 2

### Example

### Solution

The structure of the given conditional is

[if ... , then ...].

So the statement behind if is p:

he is not in his room.

And the statement behind then is q:

he is playing basketball.

The given conditional statement is p → q.

Then the converse is,

switch p and q,

q → p.

Write the converse q → p.

If, q, he is playing basketball,

then, p, he is not in his room.

So the converse is

if he is playing basketball,

then he is not in his room.