Answer
We will use the rule of universal instantiation on the premise involving universal quantifier. Then use modus tollens to prove the conclusion.
Work Step by Step
1.) $\forall x (P(x) \rightarrow Q(x))$ {Hypothesis}
2.) $P(a) \rightarrow Q(a)$ {Universal Instantiation}
3.) $\lnot Q(a)$ {Hypothesis}
4.) $\lnot P(x)$ {Modus tollens from 3.) and 2.) }
Hence, we have proved that Premises $\forall x (P(x) \rightarrow Q(x))$ and $\lnot Q(a)$ leads to conclusion $\lnot P(x)$. This justifies rule of Universal modus tollens.
