JEE Main 2023 (Online) 10th April Evening ShiftQuestion 1
Let $A=\{2,3,4\}$ and $B=\{8,9,12\}$. Then the number of elements in the relation $R=\{((a_1,b_1),(a_2,b_2))\in(A\times B,A\times B):a_1\text{ divides }b_2\text{ and }a_2\text{ divides }b_1\}$ is
Sets, Relations and Function
Solution
$(a_1,b_1),(a_2,b_2)$ range over 9 pairs each. Counting with $a_1|b_2$ and $a_2|b_1$ over all $81$ ordered pairs gives 36. Option (D).