Question:
If \( N \) denote the set of all natural numbers and \( R \) the relation on \( N \times N \) defined by \( (a, b) R (c, d) \), if \( a(b + c) = b(a + d) \), then \( R \) is
If \( N \) denote the set of all natural numbers and \( R \) the relation on \( N \times N \) defined by \( (a, b) R (c, d) \), if \( a(b + c) = b(a + d) \), then \( R \) is
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An equivalence relation must be reflexive, symmetric, and transitive.
Updated On: Jan 6, 2026
- symmetric only
- reflexive only
- transitive only
- an equivalence relation
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Verifying equivalence properties.
The relation satisfies the reflexive, symmetric, and transitive properties. Therefore, it is an equivalence relation.
Step 2: Conclusion.
The correct answer is that the relation is an equivalence relation, corresponding to option (4).
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