Given the following digraph the represents a relation is thi

Given the following digraph the represents a relation, is this relation equivalence? Yes/no. And explain why?

Solution

Answer :

Since at each vertex in the graph has a loop. hence the relation represented bt the graph is reflexive.

since there is an edge from the vertex a to the vertex b and an edge from the vertex b to the vertex a .

since there is an edge from the vertex c to the vertex d and an edge from the vertex d to the vertex c .

So , the relation represented by the graph is symmetric.

And the relation represented by the graph is transitive also .

As the relation is reflexive , symmetric and transitive it is an equivalence relation.