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- Contraposition abstract "For contraposition in the field of traditional logic, see Contraposition (traditional logic). For contraposition in the field of symbolic logic, see Transposition (logic).In logic, contraposition is a law, which says that a conditional statement is logically equivalent to its contrapositive. The contrapositive of the statement has its antecedent and consequent inverted and flipped: the contrapositive of is thus . For instance, the proposition "All bats are mammals" can be restated as the conditional "If something is a bat, then it is a mammal". Now, the law says that statement is identical to the contrapositive "If something is not a mammal, then it is not a bat."The contrapositive can be compared with three other relationships between conditional statements:Inversion (the inverse): ."If something is not a bat, then it is not a mammal." Unlike the contrapositive, the inverse's truth value is not at all dependent on whether or not the original proposition was true, as evidenced here. The inverse here is clearly not true.Conversion (the converse): . "If something is a mammal, then it is a bat." The converse is actually the contrapositive of the inverse and so always has the same truth value as the inverse, which is not necessarily the same as that of the original proposition.Negation: ."There exists a bat that is not a mammal. " If the negation is true, the original proposition (and by extension the contrapositive) is untrue. Here, of course, the negation is untrue.Note that if is true and we are given that Q is false, , it can logically be concluded that P must be false, . This is often called the law of contrapositive, or the modus tollens rule of inference.".
- Contraposition thumbnail Venn_A_subset_B.svg?width=300.
- Contraposition wikiPageID "8556497".
- Contraposition wikiPageRevisionID "602814592".
- Contraposition hasPhotoCollection Contraposition.
- Contraposition subject Category:Mathematical_logic.
- Contraposition subject Category:Theorems_in_propositional_logic.
- Contraposition type Abstraction100002137.
- Contraposition type Communication100033020.
- Contraposition type Message106598915.
- Contraposition type Proposition106750804.
- Contraposition type Statement106722453.
- Contraposition type Theorem106752293.
- Contraposition type TheoremsInPropositionalLogic.
- Contraposition comment "For contraposition in the field of traditional logic, see Contraposition (traditional logic). For contraposition in the field of symbolic logic, see Transposition (logic).In logic, contraposition is a law, which says that a conditional statement is logically equivalent to its contrapositive. The contrapositive of the statement has its antecedent and consequent inverted and flipped: the contrapositive of is thus .".
- Contraposition label "Bewijs door contrapositie".
- Contraposition label "Contraposición lógica".
- Contraposition label "Contraposition".
- Contraposition label "Contraposição".
- Contraposition label "Kontraposition".
- Contraposition label "Prawo kontrapozycji".
- Contraposition label "Proposition contraposée".
- Contraposition label "Закон контрапозиции".
- Contraposition label "対偶 (論理学)".
- Contraposition label "換質換位律".
- Contraposition sameAs Kontraposition.
- Contraposition sameAs Contraposición_lógica.
- Contraposition sameAs Proposition_contraposée.
- Contraposition sameAs 対偶_(論理学).
- Contraposition sameAs 대우_(논리학).
- Contraposition sameAs Bewijs_door_contrapositie.
- Contraposition sameAs Prawo_kontrapozycji.
- Contraposition sameAs Contraposição.
- Contraposition sameAs m.0277s2n.
- Contraposition sameAs Q1077442.
- Contraposition sameAs Q1077442.
- Contraposition sameAs Contraposition.
- Contraposition wasDerivedFrom Contraposition?oldid=602814592.
- Contraposition depiction Venn_A_subset_B.svg.
- Contraposition isPrimaryTopicOf Contraposition.
