Let A, B, and C be sets. Using Venn Diagram and Set identities, show that a) (A∪B)⊆ (A∪B ∪C). b) (A∩B ∩C)⊆ (A∩B). c) (A−B)−C ⊆ A−C.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 1E
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Let A, B, and C be sets. Using Venn Diagram and Set identities, show that

a) (A∪B)⊆ (A∪B ∪C).

b) (A∩B ∩C)⊆ (A∩B).

c) (A−B)−C ⊆ A−C.

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