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JEE Mathematics · Hard

Sets, Relations and Functions: Equivalence relation MCQ

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Equivalence relationHardQuestion 410008

Question

An equivalence relation must be:
  1. A
    Reflexive, symmetric, and transitive
    Correct
  2. B
    Only symmetric
  3. C
    Only transitive
  4. D
    Reflexive and antisymmetric

Correct answer

Reflexive, symmetric, and transitive

Explanation

Equivalence relation: (1) Reflexive: aRa. (2) Symmetric: aRb → bRa. (3) Transitive: aRb and bRc → aRc. Example: equality (=), congruence modulo n.

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