. Let A = {1,2,3,4}, let S = P(A) and let R ⊆ S x S be a relation defined by the rule (X,Y) ∈ R ⇔ (X ∩ Y = Ø) ∧ (X ∪ Y = A). (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 A = {1,2,3,4}, let S = P(A) and let R ⊆ S x S be a relation defined by the rule (X,Y) ∈ R ⇔ (X ∩ Y = Ø) ∧ (X ∪ Y = A). (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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