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

- A
${2^{99}}$

- B
${99^2}$

- C
$100$

- D
$18$

If $P=\{a, b, c\}$ and $Q=\{r\},$ form the sets $P \times Q$ and $P \times Q$ Are these two products equal?

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

$A \times(B \cup C)$

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

If $A = \{ x:{x^2} - 5x + 6 = 0\} ,\,B = \{ 2,\,4\} ,\,C = \{ 4,\,5\} ,$ then $A \times (B \cap C)$ is

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

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 $y \in B.$