Let R be a relation on the set of natural numbers N defined by nRm if n divides m. Then R is :
(A) Reflexive Relation
(B) Symmetric Relation
(C) Transitive Relation
(D) Identity Relation
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 1
The correct answer is option (1) → (A) and (C) Only
R is reflexive
as for every x ∈ real no.
$\frac{x}{x}=1$ (divisible) so $(x,x)∈R$
R is not symmetric
eq: $(1,2)∈R$ but $(2,1)∉R$
R is transitive
as $(x,y)∈R,(y,z)∈R$
⇒ z divisible by y, y divisible by x
⇒ z divisible by x
so $(x,z)∈R$
only A, C correct