Question

If relations $R_{1} \, and \, R_{2}$ from set $A$ to set $B$ are defined as $R_{1}=\left\{\left(1 , 2\right) , \, \left(3 , 4\right) , \, \left(5 , 6\right)\right\}$ and $R_{2}=\left\{\left(2 , 1\right) , \, \left(4 , 3\right) , \, \left(6 , 5\right)\right\}$ , then $n\left(A \times B\right)$ can be equal to

• A. $35$
• B. $53$
• C. $91$
• D. $55$

Answer 1

Answer: (C)

$n\left(A \times B\right)=n\left(A\right)\times n\left(B\right)$
Now minimum $n\left(A\right)=6$ and minimum $n\left(B\right)=6$
$\Rightarrow n\left(A\right)\times n\left(B\right)$ can be equal to $7\times 13=91$