Let A = {2, 3, 4} and B = {8, 9, 12}. Then the number of elements in the relation R = {((a1, b1), (a2, b2)) ∈ (A × B, A × B) : a1 divides b2 and a2 divides b1} is
- 12
- 18
- 24
- 36
The Correct Option is D
Solution and Explanation
Step 1: Divisibility conditions
We are given two sets \( A = \{2, 3, 4\} \) and \( B = \{8, 9, 12\} \). We need to find the number of elements in the relation where \( a_1 \) divides \( b_2 \) and \( a_2 \) divides \( b_1 \).
Step 2: Divisibility for \( a_1 \) dividing \( b_2 \)
For each \( a_1 \in A \), there are 2 elements in \( B \) that satisfy the divisibility condition.
Step 3: Divisibility for \( a_2 \) dividing \( b_1 \)
For each \( a_2 \in A \), there are 2 elements in \( B \) that satisfy the divisibility condition.
Step 4: Total number of relations
Each element in \( A \) has 2 choices for divisibility with elements in \( B \), so the total number of relations is: \[ \text{Total} = 6 \times 6 = 36 \] Thus, the number of elements in the relation is 36.
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