JEE Mains · Maths · STD 12 - 1. relation and function
Let \(A = \{1, 4, 7\}\) and \(B = \{2, 3, 8\}\). Then the number of elements, in the relation \(R = \{((a_1, b_1), (a_2, b_2)) \in ((A \times B) \times (A \times B)) : a_1 + b_2 \text{ divides } a_2 + b_1\}\) is _______.
- A 18
- B 36
- C 50
- D 84
Answer & Solution
Correct Answer
(A) 18
Step-by-step Solution
Detailed explanation
Let \(A = \{1, 4, 7\}\) and \(B = \{2, 3, 8\}\). The relation \(R\) consists of pairs \(((a_1, b_1), (a_2, b_2))\) from \(A \times B\) such that \((a_1 + b_2)\) divides \((a_2 + b_1)\). Let \(x = a_1 + b_2\) and \(y = a_2 + b_1\). Note that \((a_1, b_2)\) and \((a_2, b_1)\) are…
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