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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). Logic (from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy amongst philosophers (see below). ...
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. Image of a woman on the Pioneer plaque sent to outer space. ...
Binomial name Homo sapiens Linnaeus, 1758 Subspecies Homo sapiens idaltu (extinct) Homo sapiens sapiens Human beings define themselves in biological, social, and spiritual terms. ...
A truth table makes it clear that S and the inverse of S are not logically equivalent: Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ...
Truth Table for an Implication and Its Inverse | 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: Converse, Contrapositive, Denying the antecedent. In logic, if S is a statement of the form P implies Q, then the converse of S is a statement of the form Q implies P. In general, the verity of S says nothing about the verity of its converse. ...
In predicate logic, the contrapositive (or transposition) of the statement p implies q is not-q implies not-p. ...
Denying the antecedent is a type of logical fallacy. ...
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