Predicate logic : translate Everyone knows some hard-working people

Question

I am stuck with my course work as an undergraduate. It says to write the following statement in the form of predicate logic. The statement is "e. Everyone knows some hard-working people." The one I wrote is "$∀x \space ∃y(People(x) ∧ People(y) ∧ (Hardworking(y) ∧Knows(x, y)))$" Is this correct??

Answer 1

With these questions, there could potentially be a lot of correct answers, depending on how you define your variables.

One solution is to denote $P$ as the set of all people. Then we want to write something like "for any person x, there's another person y that is hardworking and that is known by x." Writing this in the mathematical logic notation, we would get $\forall x \in P, \exists y \in P \ni (Hardworking(y) \wedge Knows(x,y))$.