Prove that $(p \to q) \to (\neg q \to \neg p)$ is a tautology using the law of logical equivalence I'm new to discrete maths and I have been trying to solve this:

Decide whether $$(p \to q) \to (\neg q \to \neg p)$$ is a tautology or not by using the law of logical equivalence

I have constructed the truth table and concluded that it is indeed a tautology. However, I am having difficulty proving it using the law of logical equivalence.
I can only realize that I can use $$(p \to q ) \equiv (\neg p \lor q)$$ but after that I have no idea how to continue. Any help would be appreciated.

They're indeed equivalent (implication goes both ways). In fact
$$
p\Rightarrow q \equiv \neg(p \land \neg q)
$$
and
$$
\neg q \Rightarrow \neg p \equiv \neg (\neg q \land \neg \neg p)\equiv \neg (p \land \neg q)
$$
So the two are equal, and therefore one implies the other.
