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 $A$ and $B$ are any two non-empty sets and $A$ is a proper subset of $B$. If $n(A) = 4$,then the minimum possible value of $n(A \Delta B)$ is (where $\Delta$ denotes the symmetric difference of set $A$ and set $B$).

Set $A$ has $m$ elements and Set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$,then the value of $m \times n$ is

If $A = \{a, b\}$,$B = \{c, d\}$,$C = \{d, e\}$,then the set $\{(a, c), (a, d), (a, e), (b, c), (b, d), (b, e)\}$ is equal to:

The set $A = \{ x: x \in R, x^2 = 16 \text{ and } 2x = 6 \}$ equals

If $S$ and $T$ are two sets such that $S$ has $21$ elements,$T$ has $32$ elements,and $S \cap T$ has $11$ elements,how many elements does $S \cup T$ have?