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Exercise 17.2.18. Find binary relations on {1,2,3} that meet each of the following conditions. Express each relation as a set of ordered pairs, and draw the corresponding digraph. (Note: each part can have more than one answer, but you only need to find one.) (a) symmetric, but neither reflexive nor transitive. (b) reflexive, but neither symmetric nor transitive. (c) transitive and symmetric, but not reflexive.

Exercise 17.2.18. Find binary relations on {1,2,3} that meet each of the following conditions. Express each relation as a set of ordered pairs, and draw the corresponding digraph. (Note: each part can have more than one answer, but you only need to find one.) (a) symmetric, but neither reflexive nor transitive. (b) reflexive, but neither symmetric nor transitive. (c) transitive and symmetric, but not reflexive.

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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Please do Exercise 17.2.18 part A,B,C,and D. Please show step by step and explain

Exercise 17.2.18. Find binary relations on {1,2,3} that meet each of the following conditions. Express each relation as a set of ordered pairs, and draw the corresponding digraph. (Note: each part can have more than one answer, but you only need to find one.) (a) symmetric, but neither reflexive nor transitive. (b) reflexive, but neither symmetric nor transitive. (c) transitive and symmetric, but not reflexive. (d) neither reflexive, nor symmetric, nor transitive.
Transcribed Image Text:Exercise 17.2.18. Find binary relations on {1,2,3} that meet each of the following conditions. Express each relation as a set of ordered pairs, and draw the corresponding digraph. (Note: each part can have more than one answer, but you only need to find one.) (a) symmetric, but neither reflexive nor transitive. (b) reflexive, but neither symmetric nor transitive. (c) transitive and symmetric, but not reflexive. (d) neither reflexive, nor symmetric, nor transitive.
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