Predicate logic using sets instead of predicate functions

Question

Let $\mathit{L}$ be the set of Lions, $\mathit{M}$ the set of Mammals and $\mathit{A}$ the set of all Animals. Use rules of inference with quantifiers to formalize the following statement:

$\mathit{S}$: "If an animal is a Lion, then, they must also be a Mamal"

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Here is my answer to this problem:

Universe of discourse is defined as $\mathit{A}$, then:

$\forall x(x \in L \to x \in M)$

Now, my issue is that I've never seen sets used in predicate logic like this, usually I am given predicate functions instead, such as $\mathit{L(x)}$: "x is a Lion". Then an answer will look more like this :

$\forall x(L(x) \to M(x))$

I've been told that I don't need to create my own predicate functions to solve the exercise so my question is. Is my answer above using sets correct? Is that the correct syntax for using set notation with quantifiers and rules of inference ? Is it equivalent to the answer using predicate functions?

Thanks in advance

Answer 1

$\forall x(x \in L \to x \in M)$ seems to be the correct answer here, since the exercise doesn't require you to write a formula in a given language.