In logic,
contraposition is a law, which says that a conditional statement is logically equivalent to its contrapositive. The
Kaynak: ContrapositionIn traditional logic ,
contraposition is a form of immediate inference in which from a given proposition another is inferred having for
Kaynak: Contraposition (traditional logic)Transposition and the method of
contraposition: applied to categorical propositions through
contraposition and obversion a series of
Kaynak: Transposition (logic)In other words, to prove by
contraposition that P Rightarrow Q, prove that lnot Q Rightarrow lnot P. Any proof by contrapositive can
Kaynak: Proof by contrapositiveFor example, in intuitionistic logic which rejects proofs by
contraposition as valid rules of inference, (p → q) ⇒ ¬p ∨ q is not a
Kaynak: Material conditionalContraposition:
Contraposition (traditional logic) immediate inference that "All non-P are non-S" which is the
contraposition of the given statement.
Kaynak: Immediate inference contraposition fails. A semantic interpretation of conditional quantifiers involves a relation between sets of subsets of a given structure—
Kaynak: Conditional quantifier In strict logic al terms, via
contraposition , this statement is equivalent to. (2) Everything that is not black is not a raven.
Kaynak: Raven paradoxPopular rules of inference include modus ponens, modus tollens from propositional logic and
contraposition . First-order predicate logic
Kaynak: Rule of inferenceWe want to show: If G implies A, then G proves A. We proceed by
contraposition : We show instead that if G does not prove A then G does not
Kaynak: Propositional calculusSyntactically, (1) and (2) are derivable from each other via the rules of
contraposition and double negation . Semantically, (1) and (2)
Kaynak: Logical equivalence