Let R be a relation on the set of all natural numbers given by a R b

1.	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. ReflexivityII. Symmetry III. Transitivity(A) I only(B) III only (C) I and III only (D) I and II only
Answer» Correct option (A) I only Explanation: (I) This relation is reflexive relation because every natural no. divides square of itself a R a ⇔ a divides a² (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

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. ReflexivityII. Symmetry III. Transitivity(A) I only(B) III only (C) I and III only (D) I and II only

Answer»

Correct option (A) I only

Explanation:

(I) This relation is reflexive relation because every natural no. divides square of itself

a R a ⇔ a divides a²

(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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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. ReflexivityII. Symmetry III. Transitivity(A) I only(B) III only (C) I and III only (D) I and II only

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