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1.Relation and Function
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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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