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Contraposition

Contraposition Con"tra*po*si"tion, n. [Pref. contra- + position: cf. f. conterposition.] 1. A placing over against; opposite position. [Obs.] --F. Potter. 2. (Logic) A so-called immediate inference which consists in denying the original subject of the contradictory predicate; e.g.: Every S is P; therefore, no Not-P is S.

Contraposition Con"tra*po*si"tion, n. [Pref. contra- + position: cf. f. conterposition.] 1. A placing over against; opposite position. [Obs.] --F. Potter. 2. (Logic) A so-called immediate inference which consists in denying the original subject of the contradictory predicate; e.g.: Every S is P; therefore, no Not-P is S.

- In logic and mathematics, contraposition refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and...

- In traditional logic, contraposition is a form of immediate inference in which a proposition is inferred from another and where the former has for its...

- and vice versa. In mathematics, proof by contrapositive, or proof by contraposition, is a rule of inference used in proofs, where one infers a conditional...

- criticized in the phrase: absence of evidence is not evidence of absence. Contraposition is a logically valid rule of inference that allows the creation of a...

- a rule of inference is applied to categorical propositions through contraposition and obversion, a series of immediate inferences where the rule of obversion...

- argument: affirming the consequent and denying the antecedent. See also contraposition and proof by contrapositive. The form of a modus tollens argument resembles...

- smaller series, Σ a n {\displaystyle \Sigma a_{n}} must converge. By contraposition, if the red series Σ a n {\displaystyle \Sigma a_{n}} is proven to diverge...

- statement. There are several operations (e.g., conversion, obversion, and contraposition) that can be performed on a categorical statement to change it into...

- is often used instead of "proof by mathematical induction". Proof by contraposition infers the statement "if p then q" by establishing the logically equivalent...

- inference in propositional logic include modus ponens, modus tollens, and contraposition. First-order predicate logic uses rules of inference to deal with logical...

- In traditional logic, contraposition is a form of immediate inference in which a proposition is inferred from another and where the former has for its...

- and vice versa. In mathematics, proof by contrapositive, or proof by contraposition, is a rule of inference used in proofs, where one infers a conditional...

- criticized in the phrase: absence of evidence is not evidence of absence. Contraposition is a logically valid rule of inference that allows the creation of a...

- a rule of inference is applied to categorical propositions through contraposition and obversion, a series of immediate inferences where the rule of obversion...

- argument: affirming the consequent and denying the antecedent. See also contraposition and proof by contrapositive. The form of a modus tollens argument resembles...

- smaller series, Σ a n {\displaystyle \Sigma a_{n}} must converge. By contraposition, if the red series Σ a n {\displaystyle \Sigma a_{n}} is proven to diverge...

- statement. There are several operations (e.g., conversion, obversion, and contraposition) that can be performed on a categorical statement to change it into...

- is often used instead of "proof by mathematical induction". Proof by contraposition infers the statement "if p then q" by establishing the logically equivalent...

- inference in propositional logic include modus ponens, modus tollens, and contraposition. First-order predicate logic uses rules of inference to deal with logical...

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