Contrapositive of a Conditional Statement

Contrapositive of a Conditional Statement

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

How to Find

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

The contrapositive of a pq is ~q → ~p.

To find the contrapositive,
negate and switch both p and q.

Conditional statement: hypothesis and conclusion

Example 1

Write the contrapositive 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 ~q → ~p:
If 2 is not an odd number (~q),
then 2 is not a prime number (~p).

Example 2

Write the contrapositive 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 ~q → ~p:
If he is not playing basketball,
then he is in his room.

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