Let $A, B, C$ are 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 × B) \cap  (B × C)) $ is equal to -

If two sets $A$ and $B$ have $99$ elements in common, then the number of elements common to the sets $A \times B$ and $B \times  A$ is equal to

If $R$ is the set of all real numbers, what do the cartesian products $R \times R$ and $R \times R \times R$ represent?

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

$A \times(B \cup C)$

If $P,Q$ and $R$ are subsets of a set $A$, then $R × (P^c  \cup  Q^c)^c =$