Question

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

• A. $18$
• B. $6$
• C. $4$
• D. $0$

Answer 1

Answer: (C)

$4$

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

$\therefore n(A\cap B)=2$

and we know $n[(A\times B)\cap (B\times A)]=n[(A\cap B)\times (B\cap A)]$

$\Rightarrow n[(A\times B)\cap (B\times A)]=2\times 2=4$