If $P=\{1,2\},$ form the set $P \times P \times P$

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

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

Let $A=\{1,2\}, B=\{1,2,3,4\}, C=\{5,6\}$ and $D=\{5,6,7,8\} .$ Verify that

$A \times(B \cap C)=(A \times B) \cap(A \times C)$

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

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