If the set $A$ has $3$ elements and the set $B=\{3,4,5\},$ then find the number of elements in $( A \times B ).$
It is given that set $A$ has $3$ elements and the elements of set $B$ are $3,4,$ and $5.$
$\Rightarrow$ Number of elements in set $B=3$
Number of elements in $(A \times B)$
$ = {\rm{ (}}$ Number of elements in $A) \times {\rm{ (}}$ Number of elements in $B)$
$=3 \times 3=9$
Thus, the number of elements in $(A \times B)$ in $9$
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 $A=\{-1,1\},$ find $A \times A \times A.$
If $G =\{7,8\}$ and $H =\{5,4,2\},$ find $G \times H$ and $H \times G$.
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
Let $A = \{1, 2, 3, 4, 5\}; B = \{2, 3, 6, 7\}$. Then the number of elements in $(A × B) \cap (B × A)$ is