Q. 75.0( 1 Vote )

# 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 isA. reflexive and symmetric but not transitiveB. reflexive and transitive but not symmetricC. symmetric and transitive but not reflexiveD. an equivalence relation

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)

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