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)
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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Problem 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)
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