If the set $A$ has $3$ elements and the set $B = \{3, 4, 5\},$ then find the number of elements in $(A \times B).$

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

Let $A, B, C$ be three sets such that $n(A \cap B) = n(B \cap C) = n(C \cap A) = n(A \cap B \cap C) = 2$. Then $n((A \times B) \cap (B \times C))$ is equal to -

If $(1, 3), (2, 5)$ and $(3, 3)$ are three elements of $A \times B$ and the total number of elements in $A \times B$ is $6$,then the remaining elements of $A \times B$ are

If $A = \{1, 2, 3\}$ and $B = \{3, 8\}$,then $(A \cup B) \times (A \cap B)$ is