Logic Question - Why is This an Implication?

Question

I have a question about predicate logic. Suppose we have the following predicates:

$\text{Study}(x,y)$: x studies y

$\text{Comp}(x)$: x is a computing student

I want to encode the following sentence in predicate logic: "Some, but not all computer students study logic."

A potential answer is:

$$\exists x(\text{Comp}(x)\land \text{Study}(x,l))\land\neg \forall x(\text{Comp}(x)\implies \text{Study}(x,l))$$

Why is there an $\implies$ and not a $\land$? Is this formulation correct?

Answer 1

Because $\neg\forall x\,(\text{Comp}(x) \wedge \text{Study}(x,l))$ means "It is not true that every student is both a computing student and studying logic." In particular, that would be true if there is at least one student who is not a computing student, regardless of whether all computing students do or do not study logic.