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0 votes
3.4k views
in Mathematics by (69.1k points)

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

(A)  I only

(B)  III only 

(C)  I and III only 

(D)  I and II only 

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1 Answer

+1 vote
by (73.1k points)

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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