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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram

A = {a, b, c} and relation R on A is R = {(a,a), (b,b), (c,c), (a,b), (b,a)}. Which statement is correct?

R is reflexive, symmetric and transitive, hence an equivalence relation. All self-pairs are present, (a,b) and (b,a) appear together, and the chains (a,b),(b,a) and (b,a),(a,b) need (a,a) and (b,b), which are present.

  1. AR is reflexive and symmetric but not transitive
  2. BR is reflexive, symmetric and transitiveCorrect
  3. CR is symmetric and transitive but not reflexive
  4. DR is reflexive and transitive but not symmetric

Explanation

Reflexive: (a,a), (b,b), (c,c) are all present. Symmetric: (a,b) has (b,a), and the others are self-pairs. Transitive: (a,b),(b,a) needs (a,a), present; (b,a),(a,b) needs (b,b), present; all other chains are with self-pairs and hold. So R is an equivalence relation. Saying it is not transitive misses these checks.

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