Inverse Statement

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

Definition

Definition

[~p → ~q] is the inverse
of the conditional statement [p → q].

To find the inverse,
negate both 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 inverse is,
negate both p and q,
~p → ~q.

Write the inverse ~p → ~q.

If, not p, 2 is not a prime number,

then, not q, 2 is not an odd number.

So the inverse is
if 2 is not a prime number,
then 2 is not an odd 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 inverse is,
negate both p and q,
~p → ~q.

Write the inverse ~p → ~q.

If, not p, he is in his room,

then, not q, he is not playing basketball.

So the inverse is
if he is in his room,
then he is not playing basketball.