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, 3), (3, 2), (1, 2)}. Then, R is
Given set A = {1, 2, 3}
And R = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 2), (1, 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 (1,3) ∈ R but (3,1) ∉ R
Therefore , R is not symmetric ……. (2)
Check for transitive
Here , (1,3) ∈ R and (3,2) ∈ R and (1,2) ∈ R
Therefore , R is transitive ……. (3)
Now , according to the equations (1) , (2) , (3)
Correct option will be (B)