If the set $A$ has $3$ elements and the set $B=\{3,4,5\},$ then find the number of elements in $( A \times B ).$
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 $9$
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