Which of the following is correct about a relation R on the set of natural numbers N ?
Mathematics · Class 12 · CBSE — Relations and Functions
Which of the following is correct about a relation \(R\) on the set of natural numbers \(\mathbb{N}\)?
- \(R = \phi\) is symmetric and transitive.
- \(R = \{(a, b) : a - b \geq 0, a, b \in \mathbb{N}\}\) is symmetric.
- \(R = \{(a, b) : a + b \text{ divisible by } 3\}\) is transitive.
- \(R = \{(a, a) : a \in \mathbb{N}, a \text{ is divisible by } 2\}\) is reflexive.
Answer
(A) R = is symmetric and transitive.
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