1.Relation and Function
medium

Let $A =\{2,3,4\}$ and $B =\{8,9,12\}$. Then the number of elements in the relation $R=\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right) \in(A \times B, A \times B): a_1\right.$ divides $b_2$ and $a_2$ divides $\left.b_1\right\}$ is:

A

$36$

B

$12$

C

$18$

D

$24$

(JEE MAIN-2023)

Solution

$a_1$ divides $b_2$

Each element has 2 choices

$\Rightarrow 3 \times 2=6$

$a_2$ divides $b_1$

Each element has $2$ choices

$\Rightarrow 3 \times 2=6$

$\text { Total }=6 \times 6=36$

Standard 12
Mathematics

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