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Let X = {0, 1, 2, 3, 4}. Draw a relation R on X such that xRy if x + y = 4. a. Draw the graph associated with this relation. b. Should this graph be directed or undirected?

Let X = {0, 1, 2, 3, 4}. Draw a relation R on X such that xRy if x + y = 4. a. Draw the graph associated with this relation. b. Should this graph be directed or undirected?

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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**Transcription for Educational Use** --- Let \( X = \{0, 1, 2, 3, 4\} \). Draw a relation \( R \) on \( X \) such that \( xRy \) if \( x + y = 4 \). a. Draw the graph associated with this relation. b. Should this graph be directed or undirected? --- **Explanation:** The problem asks to find a relation \( R \) on the set \( X = \{0, 1, 2, 3, 4\} \) where two elements \( x \) and \( y \) are related if their sum equals 4. **Pairs satisfying the condition \( x + y = 4 \) are:** - \( (0, 4) \) - \( (1, 3) \) - \( (2, 2) \) - \( (3, 1) \) - \( (4, 0) \) **a. Graph Explanation:** - The graph will have vertices labeled 0, 1, 2, 3, and 4. - Edges will connect the vertices based on the pairs identified: - An edge between 0 and 4 - An edge between 1 and 3 - A loop at 2 (since 2 pairs with itself) - An edge between 3 and 1 - An edge between 4 and 0 **b. Directed or Undirected Graph:** - The graph should be undirected because the relation is symmetric: if \( xRy \), then \( yRx \) for all \( x, y \) that satisfy the condition.
Transcribed Image Text:**Transcription for Educational Use** --- Let \( X = \{0, 1, 2, 3, 4\} \). Draw a relation \( R \) on \( X \) such that \( xRy \) if \( x + y = 4 \). a. Draw the graph associated with this relation. b. Should this graph be directed or undirected? --- **Explanation:** The problem asks to find a relation \( R \) on the set \( X = \{0, 1, 2, 3, 4\} \) where two elements \( x \) and \( y \) are related if their sum equals 4. **Pairs satisfying the condition \( x + y = 4 \) are:** - \( (0, 4) \) - \( (1, 3) \) - \( (2, 2) \) - \( (3, 1) \) - \( (4, 0) \) **a. Graph Explanation:** - The graph will have vertices labeled 0, 1, 2, 3, and 4. - Edges will connect the vertices based on the pairs identified: - An edge between 0 and 4 - An edge between 1 and 3 - A loop at 2 (since 2 pairs with itself) - An edge between 3 and 1 - An edge between 4 and 0 **b. Directed or Undirected Graph:** - The graph should be undirected because the relation is symmetric: if \( xRy \), then \( yRx \) for all \( x, y \) that satisfy the condition.
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