Q. 35.0( 2 Votes )

# Mark the tick against the correct answer in the following:

Let A = {1, 2, 3} and let R = {(1, 1),

(2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}. Then, R is

A. reflexive and symmetric but not transitive

B. symmetric and transitive but not reflexive

C. reflexive and transitive but not symmetric

D. an equivalence relation

Answer :

Given set A = {1, 2, 3}

And R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}

__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

Since , (1,1) ∈ R , (2,2) ∈ R , (3,3) ∈ R

Therefore , R is reflexive ……. (1)

Check for symmetric

Since , (1,2) ∈ R and (2,1) ∈ R

(2,3) ∈ R and (3,2) ∈ R

Therefore , R is symmetric ……. (2)

Check for transitive

Here , (1,2) ∈ R and (2,3) ∈ R but (1,3) ∉ R

Therefore , R is not transitive ……. (3)

Now , according to the equations (1) , (2) , (3)

Correct option will be (A)

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