Let $R, P , Q$ be relations, prove that the following statement is tautology 
Let $P, R, Q$ be relations. Prove that:
$\exists x(R(x) \vee P(x)) \to (\forall y \neg R(y) \to (\exists xQ(x)
 \to \forall x \neg P(x)))$ is a tautology.

How do I do so? please help. 

This isn't a tautology. Consider a universe with one single object such that the object satisfies $P$ and it doesn't satisfy $R$. For simplicity let $Q$ mean the same as $P$.
Then it is true that $\exists x(R(x) \lor P(x))$. It is also true that $\forall y \neg R(y)$. Furthermore it is true that $\exists xQ(x)$. However it is false that $\forall x \neg P(x)$ because of our initial hypothesis.
