Let R = {(1, 1), (2, 2), (3, 3), (1,2)} be the relation on the set {1, 2, 3}, then the minimum number of elements to be added so that R is an equivalence relation, is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1
R already contains (1, 1), (2, 2), (3, 3), so it is reflexive.
For symmetry, (2, 1) must be added. Then
R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}
This is also transitive: the only chains are (1, 2), (2, 1) giving (1, 1), and (2, 1), (1, 2) giving (2, 2), both present.
So adding just 1 element makes R an equivalence relation.