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.
