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Let $$A = \{2, 3, 4\}$$ and $$B = \{8, 9, 12\}$$. Then the number of elements in the relation $$R = \{(a_1, b_1, a_2, b_2) \in A \times B, A \times B: a_1 \text{ divides } b_2 \text{ and } a_2 \text{ divides } b_1\}$$ is
$$R = \{((a_1,b_1),(a_2,b_2)) \in A \times B \times A \times B: a_1 | b_2 \text{ and } a_2 | b_1\}$$
For each pair $$(a_1, b_2)$$ where $$a_1 | b_2$$: A={2,3,4}, B={8,9,12}.
2|8✓, 2|9✗, 2|12✓, 3|8✗, 3|9✓, 3|12✓, 4|8✓, 4|9✗, 4|12✓
Count of $$(a_1,b_2)$$ with $$a_1|b_2$$: 6 pairs.
Similarly for $$(a_2,b_1)$$ with $$a_2|b_1$$: same 6 pairs.
Total elements = 6 × 6 = 36.
The correct answer is Option 1: 36.
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