Inverse of a Conditional Statement

Inverse of a Conditional Statement

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

How to Find

To find the inverse of a conditional statement, negate both hypothesis and conclusion of the conditional.

The inverse of a pq is ~p → ~q.

To find the inverse,
negate both p and q.

Conditional statement: hypothesis and conclusion

Example 1

Write the inverse of the given statement: If 2 is a prime number, then 2 is an odd number.

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

Write the inverse of the given statement: If he is not in his room, then he is playing basketball.

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