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KCET2011MathematicsSets and Relations

Define a relation R on A= 1,2,3,4 as x R y if x divides y . R is

Options

  1. Areflexive and transitive
  2. Breflexive and symmetric
  3. Csymmetric and transitive
  4. Dequivalence

Correct answer

A. reflexive and transitive

Step-by-step solution

Given set A= 1,2,3,4 and relation, x R y if x divides y . Relation = (1,1),(2,2),(3,3),(4,4),(1,2),(1,3), , (1,4),(2,4) Reflexive We have, x R y y / x for x, y A For any x A , we have x / x x R x . Thus, x R x for all x A . So, R is reflexive on A . Symmetry R ia not symmetry because, if y / x , then x may not divide y . For example 4 / 2 but 2 / 4 . Transitive, Let x, y, z A , such that x R y and yRz. Then, x R y and y R z y x and z y z x . So, R is a transitive relation on A .

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