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

A relation R on the set S = {1, 2, 3, 4} is defined as R = {(a, b) : |a - b| = 1}. The relation R is:

R is symmetric because |a - b| = |b - a|, so whenever (a, b) is in R, so is (b, a). However, R is not transitive: (1, 2) and (2, 3) are in R, but (1, 3) is not, since |1 - 3| = 2, not 1.

  1. Atransitive but not symmetric
  2. Bsymmetric but not transitiveCorrect
  3. Cboth symmetric and transitive
  4. Dneither symmetric nor transitive

Explanation

First, identify R: (1,2), (2,1), (2,3), (3,2), (3,4), (4,3). Check symmetry: if (a,b) ∈ R, then |a - b| = 1, so |b - a| = 1, meaning (b,a) ∈ R. Thus R is symmetric. Check transitivity: (1,2) and (2,3) are in R, but (1,3) is not (since |1-3| = 2 ≠ 1). So R is not transitive. R is symmetric but not transitive.

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