This is a valid argument since it is not possible for the conclusion to be false if the premises are true. Supposing that the premises are both true (the dog will bark if it detects an intruder, and does indeed not bark), it follows that no intruder has been detected. Therefore, no intruder was detected by the dog. If the dog detects an intruder, the dog will bark. From these two premises it can be logically concluded that P, the antecedent of the conditional claim, is also not the case.
The second premise is an assertion that Q, the consequent of the conditional claim, is not the case. The first premise is a conditional ("if-then") claim, such as P implies Q. The form of a modus tollens argument resembles a syllogism, with two premises and a conclusion: See also contraposition and proof by contrapositive. There are two similar, but invalid, forms of argument: affirming the consequent and denying the antecedent. Modus tollens is closely related to modus ponens. The first to explicitly describe the argument form modus tollens was Theophrastus. The history of the inference rule modus tollens goes back to antiquity. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. Modus tollens takes the form of "If P, then Q. In propositional logic, modus tollens ( / ˈ m oʊ d ə s ˈ t ɒ l ɛ n z/) ( MT), also known as modus tollendo tollens ( Latin for "method of removing by taking away") and denying the consequent, is a deductive argument form and a rule of inference. Existential generalization / instantiation.Universal generalization / instantiation.
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