(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
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: