If the set $A$ has $p$ elements, $B$  has $q$ elements, then the number of elements in $A × B$ is

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 -

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

$A \times(B \cup C)$

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

$A \times(B \cap C)$

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 $y \in B.$

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