Give an example of 4 non-empty sets, A, B, C and D such that all the following are true: A ∩ B ̸ = ∅, C ∩ D = ∅ B ∈ C, A ∈ D B ⊆ C, A ̸ ⊂ D A ⊆ N, B ⊆ N i. Write the sets out explicitly in terms of the elements, i.e., do not write “A”, “B” as members of any of the sets. ii. After writing the sets out, show that each of the conditions are satisfied with brief explana- tions where appropriate.

Give an example of 4 non-empty sets, A, B, C and D such that all the following are true: A ∩ B ̸ = ∅, C ∩ D = ∅ B ∈ C, A ∈ D B ⊆ C, A ̸ ⊂ D A ⊆ N, B ⊆ N i. Write the sets out explicitly in terms of the elements, i.e., do not write “A”, “B” as members of any of the sets. ii. After writing the sets out, show that each of the conditions are satisfied with brief explana- tions where appropriate.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 21E: In Exercises 20-22, Suppose and are positive integers, is a set with elements, and is a set...

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