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Inverse (logic) - Definition and Overview |
| Related Words: Anti, Antipodal, Antipode, Antipodes, Antithesis, Antonym, Balancing, Change, Contra, Contradictory, Contrapositive, Contrary |
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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).
S and its inverse are not logical equivalents. For example, let S be the true statement "If I am a human, then I am mortal." The inverse of S is the statement "If I am not a human, then I am not mortal," which is not necessarily true.
A truth table makes it clear that S and the inverse of S are not logically equivalent:
Truth Table for an Implication and Its Inverse
| P | Q | ¬P | ¬Q | P→Q | ¬P→¬Q
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| T | T | F | F | T | T
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| T | F | F | T | F | T
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| F | T | T | F | T | F
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| F | F | T | T | T | T
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See also: Converse, Contrapositive, Denying the antecedent.
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Example Usage of Inverse |
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CardosoRT: @nickellis brastem Inverse. tinha que ser de são-paulino ;) |
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Cardoso: @nickellis brastem Inverse. tinha que ser de são-paulino ;) |
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rcobrabr: http://twitpic.com/rkxge - Brasstemp Inverse - Tks Brastemp |
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