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For each of the following relations, determine whether the relation is: (i) Reflexive. (ii) Anti-reflexive. (iii) Symmetric. (iv) Anti-symmetric. (v) Transitive. (vi) A partial order. (vii) A strict order. (viii) An equivalence relation. Justify all your answers. You need to have eight answers for each question. a The domain of R is a group of students. Ry if x has earned more credits than y. (NOTE: You can assume there are at least two students who have not earned the same number of credits.) b R is a relation on Z such that Ry if and only if x - y = 3m for some integer m. c The domain R is the set of all cell phone towers in a network. Two towers can communicate if they are within a distance of three miles from each other. Ry if x can communicate with y. (NOTE: You can assume that there are at least two towers that are within three miles of each other.)

For each of the following relations, determine whether the relation is: (i) Reflexive. (ii) Anti-reflexive. (iii) Symmetric. (iv) Anti-symmetric. (v) Transitive. (vi) A partial order. (vii) A strict order. (viii) An equivalence relation. Justify all your answers. You need to have eight answers for each question. a The domain of R is a group of students. Ry if x has earned more credits than y. (NOTE: You can assume there are at least two students who have not earned the same number of credits.) b R is a relation on Z such that Ry if and only if x - y = 3m for some integer m. c The domain R is the set of all cell phone towers in a network. Two towers can communicate if they are within a distance of three miles from each other. Ry if x can communicate with y. (NOTE: You can assume that there are at least two towers that are within three miles of each other.)

Database Systems: Design, Implementation, & Management
Database Systems: Design, Implementation, & Management
12th Edition
ISBN:9781305627482
Author:Carlos Coronel, Steven Morris
Publisher:Carlos Coronel, Steven Morris
Chapter4: Entity Relationship (er) Modeling
Section: Chapter Questions
Problem 20RQ: Describe precisely the composition of the DEPENDENT weak entitys primary key. Use proper terminology...
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For each of the following relations, determine whether the relation is: (i) Reflexive. (ii) Anti-reflexive. (iii) Symmetric. (iv) Anti-symmetric. (v) Transitive. (vi) A partial order. (vii) A strict order. (viii) An equivalence relation. Justify all your answers. You need to have eight answers for each question. a The domain of R is a group of students. Ry if x has earned more credits than y. (NOTE: You can assume there are at least two students who have not earned the same number of credits.) b R is a relation on Z such that Ry if and only if x - y = 3m for some integer m. c The domain R is the set of all cell phone towers in a network. Two towers can communicate if they are within a distance of three miles from each other. Ry if x can communicate with y. (NOTE: You can assume that there are at least two towers that are within three miles of each other.)
Transcribed Image Text:For each of the following relations, determine whether the relation is: (i) Reflexive. (ii) Anti-reflexive. (iii) Symmetric. (iv) Anti-symmetric. (v) Transitive. (vi) A partial order. (vii) A strict order. (viii) An equivalence relation. Justify all your answers. You need to have eight answers for each question. a The domain of R is a group of students. Ry if x has earned more credits than y. (NOTE: You can assume there are at least two students who have not earned the same number of credits.) b R is a relation on Z such that Ry if and only if x - y = 3m for some integer m. c The domain R is the set of all cell phone towers in a network. Two towers can communicate if they are within a distance of three miles from each other. Ry if x can communicate with y. (NOTE: You can assume that there are at least two towers that are within three miles of each other.)
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