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CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity

Let A = {1, 2, 3, 4}. The relation R = {(1,1), (2,2), (3,3), (4,4), (1,3), (3,1)} on A is:

R is an equivalence relation. It contains every pair (a, a), so it is reflexive; the pair (1,3) has its reverse (3,1), so it is symmetric; and every chain of pairs produces a pair already in R, so it is transitive.

  1. AReflexive and symmetric but not transitive
  2. BAn equivalence relationCorrect
  3. CSymmetric and transitive but not reflexive
  4. DReflexive and transitive but not symmetric

Explanation

All four pairs (a, a) are present, so R is reflexive. (1,3) and (3,1) are both present, so R is symmetric. Chains such as (1,3),(3,1) give (1,1), which is present, and (3,1),(1,3) give (3,3), also present, so R is transitive. Hence it is an equivalence relation.

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