In Boolean logic, a proposition equivalent to a conditional P → Q and defined by the conditional ¬Q →¬P.

### Examples

In logic, the contraposition is a type of reasoning that consists of affirming the implication “if not B then not A” from the implication “if A then B”. The implication “if not B then not A” is called the contraposition of “if A then B”.

For example, the contraposition to the proposition “*if it rains, then the ground will be wet*” is “*if the ground is not wet, then it is not raining*“.

For example, the contraposition of the proposition “*if n is a multiple of 9, then n is not a prime number*” is “*if n is a prime number, then n is not a multiple of 9*“.