Question

If P = {a, b, c} and Q = {b, c, d} ; find number of elements in $(P\cap Q)\times P$

Answer 1

Given,

P = {a, b, c} and Q = {b, c, d}

Intersection of two sets has the elements which are common in both the sets.
So, $P\cap Q=\{b,c\}$
Cartesian product of two sets is found by forming ordered pairs.
So, $(P\cap Q)\times P=\left\{\right(b,a),(b,b),(b,c),(c,a),(c,b),(c,c\left)\right\}$.

$n\left(\right(P\cap Q)\times P)=6$