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Select the correct answerWhich rule of inference is used in each of these arguments, “If it hailstoday, the local office will be closed. The local office is not closed today. Thus, it did not hailed today.”OptionsConjunctionModus tollensHypothetical syllogismSimplification

Question

Select the correct answerWhich rule of inference is used in each of these arguments, “If it hailstoday, the local office will be closed. The local office is not closed today. Thus, it did not hailed today.”OptionsConjunctionModus tollensHypothetical syllogismSimplification

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Solution

The correct answer is Modus tollens. This rule of inference is used when you have a conditional statement (if p then q) and the denial of the consequent (not q), allowing you to infer the denial of the antecedent (not p). In this case, "If it hails today, the local office will be closed" is the conditional statement, "The local office is not closed today" is the denial of the consequent, so you can infer "Thus, it did not hail today", which is the denial of the antecedent.

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