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

Let A = {1, 2, 3} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Which of the following is correct?

R is transitive but neither reflexive nor symmetric. No pair of the form (a, a) is present, (1, 2) lacks its reverse (2, 1), and the only chain (1, 2), (2, 3) is completed by (1, 3), so transitivity holds.

  1. AR is reflexive but not transitive
  2. BR is symmetric but not reflexive
  3. CR is transitive but neither reflexive nor symmetricCorrect
  4. DR is an equivalence relation

Explanation

No pair (a, a) is in R, so R is not reflexive. (1, 2) is in R but (2, 1) is not, so R is not symmetric. For transitivity, (1, 2) and (2, 3) are in R and (1, 3) is in R, so R is transitive. It is therefore not an equivalence relation.

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