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)}

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).

answer: what are the following choices

ratio is 2 : 9

the answer is three

13.5 : 3