MATH SOLVE

3 months ago

Q:
# Draw the directed graphs representing each of the following relations: a) {(1,1), (1,2), (1,3)} b) {(1,2), (2,1), (2,2), (3,3)} c) {(1,1), (1,2), (1,3), (2,2), (2,3), (3,3)} d) {(1,3), (3,1)}

Accepted Solution

A:

Answer and Explanation:Given : Different relations.a) {(1,1), (1,2), (1,3)}
b) {(1,2), (2,1), (2,2), (3,3)}
c) {(1,1), (1,2), (1,3), (2,2), (2,3), (3,3)}
d) {(1,3), (3,1)}To find : Draw the directed graphs representing each relations?Solution : A directed graph is defined as a set of vertices that are connected together where all the edges are directed from one vertex to another.Now, We represent each relation through directed graph.a) {(1,1), (1,2), (1,3)}
Here, 1 is connected to itself, 1 is connected to 2 and 1 is connected to 3.Refer the attached figure (1).b) {(1,2), (2,1), (2,2), (3,3)}
Here, 1 is connected to 2 and 2 is connected to 1,2 is connected to itself and 3 is connected to itself.Refer the attached figure (2).c) {(1,1), (1,2), (1,3), (2,2), (2,3), (3,3)}
Here, 1 is connected to itself, 1 is connected to 2,1 is connected to 3,2 is connected to itself , 2 is connected to 3 and 3 is connected to itself.Refer the attached figure (3).d) {(1,3), (3,1)}Here, 1 is connected to 3 and 3 is connected to 1.Refer the attached figure (4).