Having difficulties understanding well formed formulas. I understand rules, but don't know how they apply to these. If they're not well formed formulas, how do I write it so that it'll be a well formed predicate formula. Please help.
1) ((∀x P(x)) ∨ (∃y Q(f (y)))) Is this a well formed formula? Is the f(y) well formed? From the rules, it looks like predicate constants are always capitalized. Does it make a difference?
2) ∀x ∃y (P(x) ∧ Q(y)) This looks like a well formed formula to me, right?
3) ∀x (P(x) → (¬∃y Q(y))) Does the ¬∃y cause any problems?