Mark the tick against the correct answer in the following:
Let R be a relation on the set N of all natural numbers, defined by a R b ⇔ a is a factor of b. Then, R is
According to the question ,
Given set N = {1, 2, 3 ,4 …..}
And R = {(a, b) : a,b ∈ N and a is a factor of b}
Formula
For a relation R in set A
Reflexive
The relation is reflexive if (a , a) ∈ R for every a ∈ A
Symmetric
The relation is Symmetric if (a , b) ∈ R , then (b , a) ∈ R
Transitive
Relation is Transitive if (a , b) ∈ R & (b , c) ∈ R , then (a , c) ∈ R
Equivalence
If the relation is reflexive , symmetric and transitive , it is an equivalence relation.
Check for reflexive
Consider , (a,a)
a is a factor of a
(2,2) , (3,3)… (a,a) where a ∈ N
Therefore , R is reflexive ……. (1)
Check for symmetric
a R b ⇒ a is factor of b
b R a ⇒ b is factor of a as well
Ex _ (2,6) ∈ R
But (6,2) ∉ R
Therefore , R is not symmetric ……. (2)
Check for transitive
a R b ⇒ a is factor of b
b R c ⇒ b is a factor of c
a R c ⇒ b is a factor of c also
Ex _(2,6) , (6,18)
∴ (2,18) ∈ R
Therefore , R is transitive ……. (3)
Now , according to the equations (1) , (2) , (3)
Correct option will be (B)