I am asked to show the following:
(a) $p \vee q \vee r$, $s \vee \neg q \vee t$ $\vdash p \vee r \vee s \vee t$
(b)$ \varphi(x) \vdash \forall \theta(x)$ if and only if $\exists x \varphi(x) \vdash \theta(x)$
For the first one I can only think of doing the truth table but that seems like a really long way to do it.
For the second one I don't really know what to do since I am not given whether x occurs free or not in the formulas and I don't really know how to come up with these types of proofs.