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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 Spring '09
 Lecturer, Arup Guha

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