Converse Statement
How to find the converse of a conditional statement: definition, 2 examples, and their solutions.
Definition
[q → p] is the converse
of the conditional statement [p → q].
To find the converse,
switch p and q.
Example
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
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.