Inverse (logic)

In logic, if S is a statement of the form\r\r\r\r\r\r\r\r

P implies Q\r\r\r\r\r\r\r\r

then the inverse of S is the statement of the form \r\r\r\r\r\r\r\r \r\r\r\r\r\r\r\r

(not P) implies (not Q). \r\r\r\r\r\r\r\r

\r\r\r\r\r\r\r\r S and its inverse are not logical equivalents.\r For example,\r\r\r\r\r\r\r let S be the statement "If I am a human, then I am mortal",\r\r\r\r\r\r\r which is true.\r\r\r\r\r\r\r The inverse of S is the statement "If I am not a human, then \r\r\r\r\r\r\r I am not mortal," which is untrue.\r\r\r\r\r\r\r \r\r\r\r\r\r\r\r

p  q   ~p ~q    p->q  ~p->~q
----------------------------
T  T    F  F  |  T      T
T  F    F  T  |  F      T
F  T    T  F  |  T      F
F  F    T  T  |  T      T

\r\r\r Clearly the two are not logically equivalent.\r\r\r\r\r\r\r \r\r\r\r\r\r\r See also: Converse, Contrapositive, Denying the antecedent.