Let R be a relation on the set of all natural numbers given by a R `hArr` a divides `b^(2)` .
Which of the following properties does R satisfy?
I . Reflexivity
II. Symmetry
III. Transitivity

Options

A. I only
B. III only
C. I and III only
D. I and II only

Answer

A

Explanation

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