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 \(\bar R\).

Short answer

The digraph of \(\bar R\) contains all the loops and directed edges that are not present in the digraph represents\(R\) and vice versa.

Step-by-step solution

Given data

\(R\) be a relation on a set \(A\).

Step 2:Obtain the directed graph represent thecomplementary relation \(\bar R\)

In accordance to the definition of complementary relation, the digraph of \(\bar R\) contains all the loops and directed edges that are not present in the digraph represents\(R\) and vice versa.