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KVPY2017MathematicsSets and Relations

Let R be a relation on the set of all natural numbers given by a R b a divides b² . Which of the following properties does R satisfy? I. Reflexivity II. Symmetry III. Transitivity

Options

  1. AI only
  2. BIII only
  3. CI and III only
  4. DI and II only

Correct answer

A. I only

Step-by-step solution

(I) This relation is reflexive relation because every natural no. divides square of itself a R a a divides a ² (II) not symmetric eg. 5 R 10 5 Divide 100 But 10 R 5 10 Divide 25 (III) Not transitivity for example if 8 R 4 & 4 R 2 8 R 2 only (I) Option

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