If $A \times B =\{(p, q),(p, r),(m, q),(m, r)\},$ find $A$ and $B$

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

$A \times C$ is a subset of $B \times D$

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

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

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

If two sets $A$ and $B$ are having $99$ elements in common, then the number of elements common to each of the sets $A \times B$ and $B \times A$ are