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

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.