By using the graph above answer the following questions Refl

By using the graph above, answer the following questions.

Reflexive---Yes or No?

Symmetric---Yes or No?

Transitive---Yes or No?

An Equivalence Relation---Yes or No?

9 Is the relation represented by the directed graph above,

Solution

Yes, the relation is reflexive as each one of a, b, c, d, e, and f is related to itself.

No, the relation is not symmetric as a is related to b but b is not related to a. The similar case holds for b and c, a and c, e and f, e and d,

a is related to b and b is related to c implies a is related to c. Similarly, e is related to d and d is related to f implies e is related to f. Hence, the relation is transitive.

In order to be an equivalence relation, reflexive, transitive and symmetric all these three properties need to be satisfied. But here the relation is not symmetric. So this is not an equivalence relation.