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 -

Suppose that the number of elements in set $A$ is $p$,the number of elements in set $B$ is $q$ and the number of elements in $A \times B$ is $7$,then $p^2+q^2=$

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 $n(A) = 3$ and $n(B) = 3$ (where $n(S)$ denotes the number of elements in set $S$). Then,the number of subsets of $(A \times B)$ having an odd number of elements is:

State whether the following statement is true or false. If the statement is false,rewrite it 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 $y \in B$.

If $A, B,$ and $C$ are three sets,then $A \times (B \cap C)$ is equal to: