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Modus tollens - Wikipedia

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In propositional logic, modus tollens (/ˈmoʊdəs ˈtɒlɛnz/) (MT), also known as modus tollendo tollens (Latin for "method of removing by taking away")[2] and denying the consequent,[3] is a deductive argument form and a rule of inference. Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q. Not Q. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument. The history of the inference rule modus tollens goes back to antiquity.[4] The first to explicitly describe the argument form modus tollens was Theophrastus.[5] Modus tollens is closely related to modus ponens. There are two similar, but invalid, forms of argument: affirming the consequent and denying the antecedent. See also contraposition and proof by contrapositive. The form of a modus tollens argument is a mixed hypothetical s

Modus tollens - Wikipedia Jump to content From Wikipedia, the free encyclopedia Rule of logical inference Modus tollens</em>"},"type":{"wt":"{{Plainlist|\n* [[Deductive reasoning|Deductive]] [[argument form]]\n* [[Rule of inference]]\n}}"},"field":{"wt":"{{Plainlist|\n* [[Classical logic]]\n* [[Propositional calculus]]\n}}"},"statement":{"wt":"<math>P</math> implies <math>Q</math>. <math>Q</math> is false. Therefore, <math>P</math> must also be false."},"symbolic statement":{"wt":"<math>P \\rightarrow Q, \\neg Q</math> <math>\\therefore\\neg P</math><ref name=\"KA\">{{Cite web |url=https://www

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