Question

The relation {(a,a),(b,b),(c,c)} on the set {a,b,c} is a -

• A. Reflexive Relation
• B. Symmetric Relation
• C. Transitive Relation
• D. Equivalence Relation
• E. all the above

Answer 1

The correct option is E

all the above

By looking at the relation, we can immediately say that it is reflexive because all the elements are connected to itself. Now since these are the only elements, we need not look for symmetric and transitive conditions. Since this relation does not violate the conditions of symmetric and transitive, we can say it is an equivalence relation also.