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.