Question

State whether each of the following statement 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 x Q = {(m, n), (n, m)}.
(ii) If A and B are non-empty sets, then A x B is a non-empty set of ordered pairs (x, y) such that x ∈ A and y ∈ B.
(iii) If A = {1, 2}, B = {3, 4}, then A x (B ∩ Φ) = Φ.

Answer 1

(i) False
If P = {m, n} and Q = {n, m}, then
P x Q = {(m, m), (m, n), (n, m), (n, n)}
(ii) True
(iii) True