Convert the following into clauses. Show all of your steps.
(a) $\exists x \forall y L(x,y)$
(b) $\forall x \exists y L(y,x)$
(c) $\forall x \forall y \{(H(x,y) \land F(y)) \Rightarrow [\neg \exists z (H(x,z) \land S(z)) ] \}$
(d) $\forall z \{ Q(z) \Rightarrow \{ \neg \forall x \exists y [P(y) \Rightarrow P(g(z,x)) ] \} \}$
I've been asked to convert these into clauses. It's been a while since I've done any questions like this, so this is a bit of a refresher.
My question is how do you remove quantifiers? This is what I've tried so far, but I'm pretty lost.
(a) $L(x, f(x))$
However, I'm unsure if I can do this since $\exists x$ is not in the scope of $\forall y$.
(b) $L(y, f(y))$
I still have a lot of learning to do in order to complete (c) and (d).
Thanks in advance.