Next week I have a final exam in math logic, then I'm trying to solve a sample exam but I'm having a difficulty.
I have a formula under predicate calculus, and I have to prove that it's a logical truth.
12 . (8%) Let $P, R, Q$ be a predicate signs. Prove that:
$\exists x (R(x)\lor P(x)) \to (\forall y \lnot R(y) \to (\exists x Q(x) \to \forall x \lnot P(x))) $
I thought to solve it using a truth table, but I've noticed that there are $5$ predicates which are $2^5 = 32$ rows and I don't think that it's the right way.
How can I prove that this predicate is logical truth?
Please help me. thanks in advance!