Let A = {2, 3, 4} and B = {8, 9, 12}. Then the number of elements in the relation divides and divides is [2023]

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Solution

Q.
Let A = {2, 3, 4} and B = {8, 9, 12}. Then the number of elements in the relation

$R = {((a_{1}, b_{1}), (a_{2}, b_{2})) \in (A \times B, A \times B) : a_{1}$ divides $b_{2}$ and $a_{2}$ divides $b_{1}}$ is [2023]

1 24

2 12

3 36

4 18

Ans.
(3)

$a_{1}$ divides $b_{2}$

Each element has 2 choices.

$\Rightarrow 3 \times 2 = 6$

$a_{2}$ divides $b_{1}$

Each element has 2 choices.

$\Rightarrow 3 \times 2 = 6$

$∴ Total number of relations is 6 \times 6 = 36$

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