linguistic:paraphrasing, stylistic:tone
Proof by contraposition

Proof by contraposition infers the statement "if p then q " by establishing the logically equivalent contrapositive statement: "if not q then not p ".

For example, contraposition can be used to establish that, given an integer x {\displaystyle x}, if x 2 {\displaystyle x^{2}} is even, then x {\displaystyle x} is even: