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 × Q = {(m, n), (n, m)}.
(ii) If A and B are non-empty sets, then A × 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 × (B ∩ Φ) = Φ.
(i) Right answer is False.
Explanation:-
If P = {m, n} and Q = {n, m}, then
P × Q = {(m, m), (m, n), (n, m), (n, n)}
(ii) Right answer is True
Explanation:-
We have the value as, P = {m, n} and Q = {n, m},
Thus, P × Q = {(m, m), (m, n), (n, m), (n, n)}
(iii) Right answer is True
Explanation:-
We know, B ∩ Φ= Φ
Thus, we have A × {B ∩ Φ}
= A × Φ = Φ
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