Let R be a relation on the set of natural numbers defined by xRy x ≤ y . Which one of the following is correct? - Mathematics MCQ Mathematics Mock Test - 3 2026 | ExamTest.live

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Let R be a relation on the set of natural numbers defined by x R y ⟺ x \leq y . Which one of the following is correct?

Solution & Step-by-step Explanation

1. Reflexive: For any x \in N, x \leq x is always true. Thus x R x .2. Symmetric: If x \leq y, it does not mean y \leq x (e.g., 3 \leq 5 but 5 \neq \leq 3). Not symmetric.3. Transitive: If x \leq y and y \leq z, then x \leq z is always true. Transitive.Thus, R is reflexive and transitive but not symmetric.

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Let R be a relation on the set of natural numbers defined by x R y ⟺ x \leq y . Which one of the following is correct?

R is reflexive, symmetric but not transitive

R is reflexive, transitive but not symmetric

R is reflexive, transitive and symmetric

R is an equivalence relation

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