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uts) Do the following for the set X = {1,2,3,4,5). 7. (a) Give an example of a relation on X that is transitive, but not symmetric. (b) Give an example of a relation on X that is reflexive and symmetric, but not transitive. (c) Give an example of an equivalence relation on X.

uts) Do the following for the set X = {1,2,3,4,5). 7. (a) Give an example of a relation on X that is transitive, but not symmetric. (b) Give an example of a relation on X that is reflexive and symmetric, but not transitive. (c) Give an example of an equivalence relation on X.

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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### Set Relations Problem Consider the set \( X = \{1, 2, 3, 4, 5\} \). Perform the following tasks: #### (a) Example of a Relation on \( X \) that is Transitive but not Symmetric Provide an example of a relation on \( X \) that satisfies the condition of being transitive but not symmetric. #### (b) Example of a Relation on \( X \) that is Reflexive and Symmetric but not Transitive Give an example of a relation that is reflexive and symmetric; however, it does not possess transitivity. #### (c) Example of an Equivalence Relation on \( X \) Offer an example of a relation on \( X \) that qualifies as an equivalence relation. This means the relation must be reflexive, symmetric, and transitive.
Transcribed Image Text:### Set Relations Problem Consider the set \( X = \{1, 2, 3, 4, 5\} \). Perform the following tasks: #### (a) Example of a Relation on \( X \) that is Transitive but not Symmetric Provide an example of a relation on \( X \) that satisfies the condition of being transitive but not symmetric. #### (b) Example of a Relation on \( X \) that is Reflexive and Symmetric but not Transitive Give an example of a relation that is reflexive and symmetric; however, it does not possess transitivity. #### (c) Example of an Equivalence Relation on \( X \) Offer an example of a relation on \( X \) that qualifies as an equivalence relation. This means the relation must be reflexive, symmetric, and transitive.
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