COT3100Hmk02 - 3 Prove this equality between two sets by...

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COT 3100 Section 2 Homework #2 Fall 2002 Lecturer: Arup Guha Assigned: 9/4/02 Due: 9/12/02 1) Determine all of the elements in the following sets: a) {n 2 | n N, n < 10} b) {4 n - 48(2) n + 512 = 0 | n N } c) {n 3 – 3n 2 + 2n | n {0,1,2,3,4}} 2) Given that our universe U has 50 elements(|U| = 50) and that A, B and C are sets such that |A| = 24, |B| = 24, |C| = 24, |(A B) C| = 7, |A B| = 16, and |(A B) C| =40, find the following values. Please show your work. (Note: if the values can not be determined given the information above, state this and give two examples(by use of a Venn Diagram) where the size of the set in question is different, but all of the above properties hold.) a) |U – ((A B) C)| b) |U – (A (B C))| c) |A C| d) |A B| e) |(C – A) – B|
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Unformatted text preview: 3) Prove this equality between two sets by using the laws of set theory AND the table method. (Note: I can not place bars of designated strings. So, for this problem I will use the ‘ ¬ ’ symbol to denote the complement of a set.) A ∪ ( (A ∪ C) ∩ B ∩ ¬ ( ¬ A ∩ C) ) = A 4) Let A, B and C be arbitrary sets. Prove that A ⊆ (( (A ∪ B) ∩ (A ∪ C) ) ∪ ( ¬ B ∪ C)). 5) In each of these questions, assume that A, B and C are sets. a) Prove or disprove: (B ⊆ C) ⇒ (B – A) ⊆ (C – A). b) Prove or disprove: ((A ⊂ B) ∧ (B ⊆ C)) ⇒ (A ⊂ C). c) Prove or disprove: ((A ⊂ C) ∧ (B ⊂ C)) ⇒ A ∪ B ⊂ C. d) Prove or disprove: ((A ⊂ B) ∧ (A ⊂ C)) ⇒ ((B ⊆ C) ∨ (C ⊆ B))....
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