Skip to content

Proof by Contrapositive

A proof technique that proves an implication by proving its logically equivalent contrapositive.

Definition

To prove \(P \Rightarrow Q\), instead prove \(\neg Q \Rightarrow \neg P\).

Why It Works

The contrapositive of an implication is logically equivalent to the original implication. That is:

\[P \Rightarrow Q \equiv \neg Q \Rightarrow \neg P\]

Example

To be written.

Backlinks