KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 4 of 120

Marks: +1, -0

Let R be a relation on the set of all naturalnumbers given by a R b ⇔ a divides b

^{2}

.
Which of the following properties does R satisfy ?
I. Reflexivity
II. Symmetry
III. Transitivity

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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