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.