Contrapostive 2001-11-16 10:38:27 2005-04-11 09:41:18 Definition \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} Given an implication of the form $$p \implies q$$ (``p implies q'') the \emph{contrapositive} of this implication is $$\neg q \implies \neg p$$ (``not q implies not p''). An implication and its contrapositive are equivalent statements. When proving a theorem, it is often more convenient or more intuitive to prove the contrapositive instead.