Law of Contrapositive

Law of Contrapositive

How to use the law of contrapositive to solve logic problems: meaning, example, and its solution.

Meaning

A conditional and its contrapositive have the same truth value.

Law of contrapositive:
A conditional (pq)
and its contrapositive (~q → ~p)
have the same truth value.

So if pq is true,
then ~q → ~p is also true.

Example

The given statements are true: If it's raining, then I'm staying home. Write a true statement that can be derived from the given statement.

p: It's raining.
q: I'm staying home.

It says pq is true.

Then, by the law of contrapositive,
~q → ~p is also true:
If I'm not staying home (~q),
then it's not raining (~p).