hw2_key - COT3100 Summer2001 Assignment #2 (Solution key)....

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COT3100 Summer’2001 Assignment #2 (Solution key). Assigned: 05/22, due: 05/31 in recitation. Total 100 pts. 1. Let P be the set of prime numbers (integers greater then 1 divisible only by 1 and itself), A be the set of even integers and let B be set of positive multiples of 5. The universal is the set of positive integers. Determine the following sets (list all elements if there are 10 or fewer elements; list their 10 smallest elements if they have more than 10) In accordance with what we are given we have P = {2, 3, 5, 7, 11, 13, 17, 19, 23, } A ={2, 4, 6, 8, 10, …} B = {5, 10, 15, 20, 25, 30, 35, …} U = {1, 2, 3, …} a) (2pts) P A P A = {2} b) (2pts) ( A B ) - P ( A B ) - P = {4, 6, 8, 10, 12, 14, 15, 16, 18, 20, …} c) (2pts) ¬ ( A B ) ¬ ( A B ) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, …} d) (2pts) ( A - B ) ( B - A ) {2, 4, 5, 6, 8, 12, 14, 15, 16, 18, …} e) (2pts) ( B - A ) P {2, 3, 5, 7, 11, 13, 15, 17, 19, 23, …} 2. Let A , B and C be any three sets. Prove or disprove the following propositions without using Venn diagrams or membership tables: a) (10pts)( A B ) C ( A C B C ) The proposition is false. It can be disproved by the following example: A = {1, 2}, B ={2, 3}, C = {2, 4}. For these sets we have the condition ( A B ) C satisfied, since A B ={2} ⊆{2, 4}. But never the less neither A = {1, 2} nor B ={2, 3}is a subset of C ={2, 4}. b)
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hw2_key - COT3100 Summer2001 Assignment #2 (Solution key)....

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