# Predicate logic : translate Everyone knows some hard-working people

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??

• Your symbols aren't showing up for me. Please use MathJax – Alexis Olson Oct 18 '16 at 4:49
• Edited the question – shamila Oct 18 '16 at 4:50
• What is x? And what is People(x)? – nivekgnay Oct 18 '16 at 5:37
• That's what I wrote and I think it is wrong. Can you tell me the write answer? – shamila Oct 18 '16 at 6:07

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 $\forall x \in P, \exists y \in P \ni (Hardworking(y) \wedge Knows(x,y))$.