State whether each of the following statement are true or false.
Question:

State whether each of the following statement are true or false. If the statement is false, rewrite the given statement correctly.

(i) If $\mathrm{P}=\{m, n\}$ and $\mathrm{Q}=\{n, m\}$, then $\mathrm{P} \times \mathrm{Q}=\{(m, n),(n, m)\}$.

(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 $A \times(B \cap \Phi)=\Phi$.

Solution:

(i) False

If $\mathrm{P}=\{m, n\}$ and $\mathrm{Q}=\{n, m\}$, then

$\mathrm{P} \times \mathrm{Q}=\{(m, m),(m, n),(n, m),(n, n)\}$

(ii) True

(iii) True