title: "Contrapositive"

Contrapositive

Definition. The contrapositive of the statement "if $P$, then $Q$" is the statement "if not $Q$, then not $P$". A statement and its contrapositive are equivalent: each says there is no situation where $P$ holds and $Q$ fails, so proving either proves both.

Flip to the contrapositive when the original hypothesis gives you nothing to compute with; forming "not $Q$" correctly is Quantifier work. Introduced in Lecture 1, Example 3.