Question:

Let $A=\{1,3,4,6,9\}$ and $B=\{2,4,5,8,10\}$. Relation $R=\{((a_1,b_1),(a_2,b_2)):\ a_1\leq b_2\ \text{and}\ b_1\leq a_2\}$ has how many elements?

180

160

Step-by-Step Solution

Key Concept: Count pairs $(a_1,b_2)$ with $a_1\leq b_2$: 16 pairs. Count $(b_1,a_2)$ with $b_1\leq a_2$: 10 pairs.

$16\times10=160$.

Correct Answer: 1