Proof by contrapositive

Proof by contrapositive is a method of mathematical proof used to establish the truth of a conditional statement. A conditional statement is typically of the form "If \( P \), then \( Q \)", which can be written symbolically as \( P \implies Q \). The contrapositive of this statement is "If not \( Q \), then not \( P \)", symbolically expressed as \( \neg Q \implies \neg P \).