Prove the following statement using element proof: 1. For any four sets A, B, C, and D, if C ⊆ (D ∪ A) and B ⊆ D^c, then C ∩ B ⊆ A 2. For any three sets A, B, and C, if A ∩ C ⊆ B, then (A − B) ∩ (C − B) = ∅ 3. For any three sets A, B, and C, if A ∪ C ⊆ B, then C × A ⊆ B × B

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 38SE: Suppose a set A has 2,048 subsets. How many distinct objects are contained in A?
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Prove the following statement using element proof: 1. For any four sets A, B, C, and D, if C ⊆ (D ∪ A) and B ⊆ D^c, then C ∩ B ⊆ A 2. For any three sets A, B, and C, if A ∩ C ⊆ B, then (A − B) ∩ (C − B) = ∅ 3. For any three sets A, B, and C, if A ∪ C ⊆ B, then C × A ⊆ B × B
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