Let A and B be subsets of R. (a) If x ∈ (A ∩ B)c, explain why x ∈ Ac ∪ Bc. This shows that (A ∩ B)c ⊆ Ac ∪ Bc. 12 Chapter 1. The Real Numbers (b) Prove the reverse inclusion (A ∩ B)c ⊇ Ac ∪ Bc, and conclude

Let A and B be subsets of R. (a) If x ∈ (A ∩ B)c, explain why x ∈ Ac ∪ Bc. This shows that (A ∩ B)c ⊆ Ac ∪ Bc. 12 Chapter 1. The Real Numbers (b) Prove the reverse inclusion (A ∩ B)c ⊇ Ac ∪ Bc, and conclude that (A ∩ B)c = Ac ∪ Bc. (c) Show (A ∪ B)c = Ac ∩ Bc by demonstrating inclusion both ways.

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Let A and B be subsets of R. (a) If x ∈ (A ∩ B)c, explain why x ∈ Ac ∪ Bc. This shows that (A ∩ B)c ⊆ Ac ∪ Bc. 12 Chapter 1. The Real Numbers (b) Prove the reverse inclusion (A …

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