Unformatted text preview: by adding 2 to each of the first 8 subsets. Thus, the answer is 2x8 = 16. 3) (7 pts) A, B, C and D are sets such that A ⊂ B and C ⊂ D. Prove that (B ∩ C) ⊂ (A ∪ D). We must show that (B ∩ C) ⊂ (A ∪ D). Essentially, we need to show that if x ∈ (B ∩ C) then x ∈ (A ∪ D). To prove this, assume that x ∈ (B ∩ C). Under this assumption, we must show that x ∈ (A ∪ D). Using the defn of intersection, we find that x ∈ B and x ∈ C. Since C ⊂ D, by the defn of subset we have that x ∈ D. But, we know by the defn of union, that x ∈ A ∪ D....
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 Spring '09
 Set Theory, Empty set, Natural number

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