I'm confused with translating english to predicate logic. An example that I couldn't really solve is this. Let $x$ be the domain of animals, $P(x)$ be the claim that $x$ is a lion, $Q(x)$ be the claim that $x$ is fierce and $R(x)$ be the claim that $x$ drinks coffee.
My guess is that "All lions are fierce" translates to $\forall x(P(x)\rightarrow Q(x))$. Is this correct? Wouldn't this imply that all lions are fierce is true as long as I don't have a lion?
How about "some lions do not drink coffee"? Would $\exists x(P(x)\rightarrow\neg R(x))$ be correct? I'm having trouble understanding what this means and I'm still debating the difference between my answers and $\exists x(P(x)\land Q(x))$.