If $A = \{ 2,\,4,\,5\} ,\,\,B = \{ 7,\,\,8,\,9\} ,$ then $n(A \times B)$ is equal to

If $\left(\frac{x}{3}+1, y-\frac{2}{3}\right)=\left(\frac{5}{3}, \frac{1}{3}\right),$ find the values of $x$ and $y$

If $A \times B=\{(a, x),(a, y),(b, x),(b, y)\} .$ Find $A$ and $B$

$A = \{1,2,3,4......100\}, B = \{51,52,53,...,180\}$, then number of elements in $(A \times B) \cap  (B \times A)$ 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 $y \in B.$

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

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