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

Let A = {1, 2, 3}. Consider the relations R1 = {(1, 2), (2, 1)}, R2 = {(1, 1), (2, 2), (3, 3), (1, 2)} and R3 = {(1, 2), (2, 3), (1, 3)}. Which of the following correctly describes them?

R1 is symmetric but not transitive because (1,1) is missing. R2 is reflexive and transitive but not symmetric since (2,1) is absent. R3 is transitive because (1,3) follows from (1,2) and (2,3), but it is not symmetric.

  1. AR1 is transitive, R2 is symmetric, R3 is transitive
  2. BR1 is symmetric but not transitive, R2 is reflexive and transitive but not symmetric, R3 is transitive but not symmetricCorrect
  3. CR1 is symmetric and transitive, R2 is reflexive and symmetric, R3 is symmetric
  4. DR1 is reflexive, R2 is transitive and symmetric, R3 is symmetric but not transitive

Explanation

R1: (1,2),(2,1) are symmetric, but transitivity needs (1,1), which is missing, so it is not transitive. R2: contains all diagonal pairs, so it is reflexive. It is transitive since the only non-diagonal pair (1,2) causes no new pair requirement. It is not symmetric since (2,1) is absent. R3: (1,2),(2,3) need (1,3), which is present, so transitive. It is not symmetric.

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