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.

Asked by Pragya Singh | 1 year ago | 114

**(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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