Question

Let R be a relation on a set V = {a,b,c,d,e} given by

R = {(a,a),(a,b),(b,a),(b,b),(a,e),(e,a),(e,e),(a,c),(a,d),(b,c),(e,d),(c,c),(d,d)}.
(a) Using the one-to-one correspondence between relations on finite sets and directed graphs, draw the directed graph corresponding to the relation R.

Answer 1

To create the directed graph for the relation R on set V, each element of V is represented as a vertex, and directed edges are drawn to represent the ordered pairs in R.

Step-by-step explanation:

The student's question involves drawing a directed graph corresponding to a given relation, R, on a set V.

To draw the directed graph, we assign each element of the set V as a vertex in the graph. The elements of V are {a,b,c,d,e}. Then, we draw a directed edge (arrow) for each ordered pair in R. For example, the ordered pair (a,b) means we draw an arrow from vertex 'a' to vertex 'b'.

Following this method, we add arrows for each of the pairs in the relation R: {(a,a), (a,b), (b,a), (b,b), (a,e), (e,a), (e,e), (a,c), (a,d), (b,c), (e,d), (c,c), (d,d)}. By including all of these pairs, our directed graph will visually represent the relation R.