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

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

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

If $A=\{1,2\}, B=\{3,4\},$ then $A \times\{B \cap \varnothing\}=\varnothing$

Let $A=\{1,2,3\}, B=\{3,4\}$ and $C=\{4,5,6\} .$ Find

$A \times(B \cup C)$

If $G =\{7,8\}$ and $H =\{5,4,2\},$ find $G \times H$ and $H \times G$.

Let $A=\{1,2\}$ and $B=\{3,4\} .$ Write $A \times B .$ How many subsets will $A \times B$ have? List them.

Let $A=\{1,2,3\}, B=\{3,4\}$ and $C=\{4,5,6\} .$ Find

$(A \times B) \cup(A \times C)$