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Which 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.”

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Which 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.”

(a) Modus tollens

(b) Conjunction

(c) Hypothetical syllogism

(d) Simplification

I have been asked this question in final exam.

Question is from Logics in chapter The Foundation: Logics and Proofs of Discrete Mathematics

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Right option is (a) Modus tollens

The explanation is: (¬N ∧ (M → N)) → ¬M is Modus tollens.

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