JEE Mains · Maths · STD 11- 2. Relation and Function
Let \(R = \{(x, y) \in \mathbb{N} \times \mathbb{N} : \log_e(x + y) \leq 2\}\). Then the minimum number of elements, required to be added in \(R\) to make it a transitive relation, is __________.
- A 10
- B 15
- C 20
- D 25
Answer & Solution
Correct Answer
(B) 15
Step-by-step Solution
Detailed explanation
Given the relation \(R = \{(x, y) \in \mathbb{N} \times \mathbb{N} : \log_e(x + y) \leq 2\}\). This condition simplifies to: \(x + y \leq e^2\) Since \(e \approx 2.718\), we have \(e^2 \approx 7.389\). As \(x, y \in \mathbb{N}\), the sum \(x + y\) must be a natural number.…
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