\(P(x)\) can be said to implicitly quantify the 202207121344# \(Q(x)\), denoted as \(P(x) \Rightarrow Q(x)\) or \(\forall x, P(x) \rightarrow Q(x)\), if every element in the truth set# of \(P(x)\) is in the truth set of \(Q(x)\).
\(P(x)\) and \(Q(x)\) can be said are identical to each other, denoted as \(P(x) \Leftrightarrow Q(x)\) or \(\forall x, P(x) \leftrightarrow Q(x)\), if their truth sets are identical.