Let S ⊆ N be the set that contains exactly all prime numbers greater than 4 and let R ⊆ S x S be the relation defined by the rule (x,y) ∈ R ⇔ |x - y| ≤ 2. (a) Prove or find a counterexample for the following properties and based on the findings from the properties, conclude whether R is a graph, partially ordered set, equivalence relation, or a function (several answers may hold simultaneously). Analyze the relation R.: antisymmetry asymmetry symmetry irreflexivity reflexivity transitivity uniqueness

Let S ⊆ N be the set that contains exactly all prime numbers greater than 4 and let R ⊆ S x S be the relation defined by the rule (x,y) ∈ R ⇔ |x - y| ≤ 2. (a) Prove or find a counterexample for the following properties and based on the findings from the properties, conclude whether R is a graph, partially ordered set, equivalence relation, or a function (several answers may hold simultaneously). Analyze the relation R.: antisymmetry asymmetry symmetry irreflexivity reflexivity transitivity uniqueness

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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