**4. Define the relation $ r $ on $ S = \{ A, B, C, D \} $ by $ r = \{ (A, B), (A, D), (B, A), (B, C), (C, A), (C, B), (D, B) \} $. Give the relation digraph for $ r $.**In this problem, you are given a set $ S $ with elements \{ A, B, C, D \} and a relation $ r $ on this set. The relation $ r $ is a set of ordered pairs. Your task is to represent this relation using a directed graph, also known as a digraph.### Explanation of the relation:- **(A, B)**: There is a directed edge from A to B.- **(A, D)**: There is a directed edge from A to D.- **(B, A)**: There is a directed edge from B to A.- **(B, C)**: There is a directed edge from B to C.- **(C, A)**: There is a directed edge from C to A.- **(C, B)**: There is a directed edge from C to B.- **(D, B)**: There is a directed edge from D to B. ### Constructing the Relation Digraph:1. **Vertices**: Represent each element of the set $ S $ as a vertex. - A, B, C, D are the vertices of the graph.2. **Edges**: For each ordered pair in the relation $ r $, draw a directed edge from the first element to the second element. - Draw an edge from A to B. - Draw an edge from A to D. - Draw an edge from B to A. - Draw an edge from B to C. - Draw an edge from C to A. - Draw an edge from C to B. - Draw an edge from D to B.This digraph visually represents the connections defined by the relation $ r $. The arrows indicate the direction of the relation between the elements.

Answered: Image /qna-images/answer/a2039a5d-f80d-4fd6-982e-3954fa8f0894.jpg

Answered: Define the relation r on S = {A, B, C,…

Define the relation r on S = {A, B, C, D} by r ={ (A,B), A,D), (B,A), (B,C), (C,A), (C,B), (D,B)}. Give the relation digraph for r. %3D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**4. Define the relation $ r $ on $ S = \{ A, B, C, D \} $ by $ r = \{ (A, B), (A, D), (B, A), (B, C), (C, A), (C, B), (D, B) \} $. Give the relation digraph for $ r $.**

In this problem, you are given a set $ S $ with elements \{ A, B, C, D \} and a relation $ r $ on this set. The relation $ r $ is a set of ordered pairs. Your task is to represent this relation using a directed graph, also known as a digraph.

### Explanation of the relation:
- **(A, B)**: There is a directed edge from A to B.
- **(A, D)**: There is a directed edge from A to D.
- **(B, A)**: There is a directed edge from B to A.
- **(B, C)**: There is a directed edge from B to C.
- **(C, A)**: There is a directed edge from C to A.
- **(C, B)**: There is a directed edge from C to B.
- **(D, B)**: There is a directed edge from D to B.

### Constructing the Relation Digraph:
1. **Vertices**: Represent each element of the set $ S $ as a vertex.
- A, B, C, D are the vertices of the graph.

2. **Edges**: For each ordered pair in the relation $ r $, draw a directed edge from the first element to the second element.
- Draw an edge from A to B.
- Draw an edge from A to D.
- Draw an edge from B to A.
- Draw an edge from B to C.
- Draw an edge from C to A.
- Draw an edge from C to B.
- Draw an edge from D to B.

This digraph visually represents the connections defined by the relation $ r $. The arrows indicate the direction of the relation between the elements.

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