Contraposition
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High Quality Content by WIKIPEDIA articles! In propositional logic, contraposition is a logical relationship between two propositions of material implication.In vernacular terms, this states "If P then Q", or, "If Socrates is a man then Socrates is human." In a conditional such as this, P is called the antecedent and Q the consequent. One statement is the contrapositive of the other just when its antecedent is the negated consequent of the other, and vice-versa.That is, "If not-Q then not-P", or more clearly, "If Q is not the case, then P is not the case." Using our example, this is rendered "...
High Quality Content by WIKIPEDIA articles! In propositional logic, contraposition is a logical relationship between two propositions of material implication.In vernacular terms, this states "If P then Q", or, "If Socrates is a man then Socrates is human." In a conditional such as this, P is called the antecedent and Q the consequent. One statement is the contrapositive of the other just when its antecedent is the negated consequent of the other, and vice-versa.That is, "If not-Q then not-P", or more clearly, "If Q is not the case, then P is not the case." Using our example, this is rendered "If Socrates is not human, then Socrates is not a man." This statement is said to be contraposed to the original, and is logically equivalent to it. Due to their logical equivalence, stating one is effectively the same as stating the other, and where one is true, the other is also true (likewise with falsity).
