Rosen(relations)

Question

Let R be a relation on a set A. Explain how to use the directed
graph representing R to obtain the directed graph
representing the complementary relation $\overline{R}$

Comments

By changing the direction of the edges?

Answer 1

$\bar{R}= U-R$
Here U is Complete Directed graph
Draw a graph where each vertices is connected to another vertices and then remove all those edges that where present in Original Graph

This will give you Compliment

A={1,2}

Eg: R={(1,1),(2,1)}

$\bar{R}=${(1,2),(2,2)}

Comments

This is the representation of the inverse of R and not compliment, I think. For complementary relation, all the directed edges and self-loops not present in G should be present in G'.

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Yes you were correct check answer now

Answer 2

Connect the unconnected vertices 

For example if  vertices a and b are not connected, then connect them as a to b and b to a

and remove edges of already connected vertices

for example if b and c are connected as b to c , then remove that edge. ( here c to b is not connected , so connect those vertices with an edge, to form the complement)