Question:

Let $A=\{2,3,4\}$, $B=\{8,9,12\}$. Let $R=\{((a_1,b_1),(a_2,b_2)):\ a_1|b_2\ \text{and}\ a_2|b_1\}$. Number of elements in $R$ is

Step-by-Step Solution

Key Concept: Find pairs $(a_1,b_2)$ where $a_1$ divides $b_2$: 6 pairs. Similarly $(a_2,b_1)$: 6 pairs. All combinations: $6\times6=36$.

36 elements.

Correct Answer: 1