Inverse (logic)
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In logic, if S is a statement of the form "P implies Q", then the inverse of S is a statement of the form "not-P implies not-Q". In other words, the inverse is the contrapositive of the converse (or, equivalently, the converse of the contrapositive).
S and its inverse are not logical equivalents. For example, let S be the true statement "If I am a woman, then I am human". The inverse of S is the statement "If I am not a woman, then I am not human," which is not necessarily true.
A truth table makes it clear that S and the inverse of S are not logically equivalent:
| 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 |
See also
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