Question

Let $A=\left\{1,2,3,4,5\right\};B=\left\{2,3,6,7\right\}$. Then the number of elements in $(A\times B)\cap (B\times A)$ is

• A. $18$
• B. $6$
• C. $4$
• D. $0$

Answer 1

The correct option is C

$4$

Determine the number of elements in $(A\times B)\cap (B\times A)$

Given, $A=\left\{1,2,3,4,5\right\};B=\left\{2,3,6,7\right\}$

$A\times B=\left\{\left(1,2\right),\left(1,3\right),\left(1,6\right),\left(1,7\right)...........\left(5.3\right),\left(5,6\right),\left(5,7\right)\right\}$

$B\times A=\left\{\left(2,1\right),\left(2,2\right),\left(2,3\right),\left(2,4\right),\left(2,5\right).........\left(7,3\right),\left(7,4\right),\left(7,5\right)\right\}$

Hence the set $A\times B\cap B\times A$ represents the common elements between $A\times B$ and $B\times A$.Therefore

$A\times B\cap B\times A=\left\{\left(2,2\right),\left(2,3\right),\left(3,2\right),\left(3,3\right)\right\}$

Therefore the number of elements in the set $A\times B\cap B\times A$ is equal to $4$

Hence, option C is the correct answer.