Currently doing some past papers and I wanted to confirm this...

For a formula to be of a predicate logic it must follow the well-formed rules.

Only (iii) is a formula of predicate logic because it follows the well-formed rules. (i) and (ii) use predicates instead of variables after the quantifiers therefore not well-formed and not a formula of predicate logic. Is there any other reasons why they may not be of predicate logic?

Which of the following expressions are formulas of predicate logic?

(i) $\forall X \, \forall Y \ (X \subseteq Y \leftrightarrow (\forall x \ x \in X \to x \in Y))$

(ii) $\forall P \ P(0) \land \forall n \ (P(n) \to P(n+1) ) \to (\forall n \, P(n))$

(iii) $\forall t\, G(P(t) \, U \, P(t))$, where $P$ is a predicate symbol.

Currently doing some past papers and I wanted to confirm this...

For a formula to be of a predicate logic it must follow the well-formed rules.

Only (iii) is a formula of predicate logic because it follows the well-formed rules. (i) and (ii) use predicates instead of variables after the quantifiers therefore not well-formed and not a formula of predicate logic. Is there any other reasons why they may not be of predicate logic?