State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly. (i) If \(P = \{m, n\}\) and \(Q = \{n, m\}\), then \(P \times Q = \{(m, n), (n, m)\}\). (ii) If \(A\) and \(B\) are non-empty sets, then \(A \times B\) is a non-empty set of ordered pairs \((x, y)\) such that \(x \in A\) and \(y \in B\). (iii) If \(A = \{1, 2\}\), \(B = \{3, 4\)\, then \(A \times (B \cap \emptyset) = \emptyset\).