Question

Given $A=\{5,6,7\}$ and $B=\{6,8,10\}$, then : $A\times (B\cap A)$

Find the number of elements in such a set.

Answer 1

Intersection of two sets has the elements common in both the sets
$A=\{5,6,7\}$ and $B=\{6,8,10\}$
Thus, $B\cap A=\left\{6\right\}$
Cartesian product of two sets contains an ordered pair of elements $A$ and $B$ respectively,
Hence, $A\times (B\cap A)=\left\{\right(5,6),(6,6),(7,6\left)\right\}$.

Thus there are $3$ elements in such a set.