1: Let A be a non-empty set. Which of the properties reflexive, irreflexive, symmetric, asymmet- ric, antisymmetric, transitive and total do the following binary relations on A have: (a) ∅ (no two elements form A are related to each other) (b) {(a, b) : a, b ∈ A, a != b} (every two different elements from A are related to each other) (c) {(a, a) : a ∈ A} (each element is related to itself and is not related to any other element)

1: Let A be a non-empty set. Which of the properties reflexive, irreflexive, symmetric, asymmet- ric, antisymmetric, transitive and total do the following binary relations on A have: (a) ∅ (no two elements form A are related to each other) (b) {(a, b) : a, b ∈ A, a != b} (every two different elements from A are related to each other) (c) {(a, a) : a ∈ A} (each element is related to itself and is not related to any other element)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.4: Binary Operations

Problem 9E: 9. The definition of an even integer was stated in Section 1.2. Prove or disprove that the set of...

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