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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

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
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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**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.
Transcribed Image Text:**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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