Mark the tick against the correct answer in the following:
Let A = {a, b, c} and let R = {(a, a), (a, b), (b, a)}. Then, R is
Given set A = {a, b, c}
And R = {(a, a), (a, b), (b, a)}
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 , (b,b) ∉ R and (c,c) ∉ R
Therefore , R is not reflexive ……. (1)
Check for symmetric
Since , (a,b) ∈ R and (b,a) ∈ R
Therefore , R is symmetric ……. (2)
Check for transitive
Here , (a,b) ∈ R and (b,a) ∈ R and (a,a) ∈ R
Therefore , R is transitive ……. (3)
Now , according to the equations (1) , (2) , (3)
Correct option will be (C)