Solution to Consider Premises: If there was a cricket match, then traveling was difficult. If they arrived … - Sikademy
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Archangel Macsika

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

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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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Question ID: mtid-5-stid-8-sqid-3212-qpid-1911