Answer to Question #178304 in Discrete Mathematics for Faizan

Question #178304

Consider

Premises: If there was a cricket match, then traveling was difficult.

If they arrived on time, then traveling was not difficult.

They arrived on time.

Conclusion: There was no cricket match.

Determine whether the conclusion follows logically from the premises. Explain by

representing the statements symbolically and using rules of inference


1
Expert's answer
2021-04-13T13:43:41-0400

Let us use the following notation:

"p=" "There was a cricket match", "q=" "Traveling was difficult", "r=" "They arrived on time".


Then the premises are "p\\to q,\\ r\\to\\overline{q}" and "r". The conclusion is "\\overline{p}."


Using to the premises "r\\to \\overline{q}" and "r" the rule of inference Modus Ponens, we conclude "\\overline{q}". Then using to "p\\to\\ q" and "\\overline{q}" the rule of inference Modus Tollens, we have the conclusion "\\overline{p}". Therefore, the conclusion follows logically from the premises.



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