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COMEDK2025MathematicsSets and RelationsActual

The relation R= (1,1),(2,2),(3,3) on the set 1,2,3 is

Options

  1. Areflexive only
  2. Ban equivalence relation
  3. Ctransitive only
  4. Dsymmetric only

Correct answer

B. an equivalence relation

Step-by-step solution

Let A = 1, 2, 3 and R = (1, 1), (2, 2), (3, 3) . A relation R is reflexive if (a, a) R for all a A . Since (1, 1), (2, 2), (3, 3) R , the relation is reflexive. A relation R is symmetric if (a, b) R (b, a) R . For all elements in R , (a, b) = (b, a) , so the condition holds trivially. Thus, the relation is symmetric. A relation R is transitive if (a, b) R and (b, c) R (a, c) R . Since the only pairs are of the form (a, a) , if (a, a) R and (a, a) R , then (a, a) R , which is true. Thus, the relation is transitive.

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