# Translating to predicate logic

I'm kind of confused on whether or not these sentences are correct or not (particularly on something being sufficient for an argument to be true vs. something being necessary)

Let:

a = alice

b = bob

Lxy = x loves y

Fxy = x fears y

1. Bob doesn't fear anyone, $\forall x \neg Fbx$

2. Everyone who loves bob fears bob, $\forall x (Lxb \rightarrow Fxb)$

• (not sure if the antecedent and consequent should be flipped)
3. No one who fears alice fears bob, $\forall x (\neg Fxa \rightarrow Fxb)$

4. If anyone loves alice, then alice loves herself, $\exists x (Lxa \rightarrow Laa)$

Thanks

(3) should be$\forall x (Fxa \rightarrow \neg Fxb)$
(4) $\exists x Lxa \rightarrow Laa$ (the quantifier should act only over the antecedent)