# Law of Contrapositive

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

## Meaning

Law of contrapositive:

A conditional (*p* → *q*)

and its contrapositive (~*q* → ~*p*)

have the same truth value.

So if *p* → *q* is true,

then ~*q* → ~*p* is also true.

## Example

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

It says *p* → *q* 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*).