Question about predicate logic I know how to represent the sentence “there is exactly one person that is happy”,
∀y∀x((Happy(x)∧Happy(y))→(x=y))
Edit: ∃x∀y(y=x↔Happy(y))
(NOW, I actually know how to represent it)
Where x and y represent a person.
However, my problem is that I can’t figure out how to say “there are exactly 3 people that are happy” in predicate logic.

You can extend this simply as: if 4 people are happy then at least one is equal to the other.
$\forall x,y,z,w((Happy(x)\land Happy(y) \land Happy(z) \land Happy(w))\rightarrow(x=y \lor x=z \lor x=w \lor y=z \lor y=w \lor z=w)) \land \exists x,y,z (Happy(x)\land Happy(y) \land Happy(z) \land x\neq y \land y\neq z \land x \neq z) $
