contrapositive

Given an implication of the form

$$p⟹q$$

(“p implies q”) the contrapositive of this implication is

$$\mathrm{\neg }q⟹\mathrm{\neg }p$$

(“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.

Title	contrapositive
Canonical name	Contrapositive
Date of creation	2013-03-22 11:59:17
Last modified on	2013-03-22 11:59:17
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	9
Author	yark (2760)
Entry type	Definition
Classification	msc 03B05