# hwk1 - A-B-C Is it the same as any of the following sets A...

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UNIVERSITY OF CALIFORNIA, SANTA BARBARA Department of Electrical and Computer Engineering ECE 139 Probability and Statistics Spring 2008 Homework Assignment #1 (Due on Monday 4/7/2008 by 6 pm in the Homework Box ) Problem # 1 . Solve 1.2.1 in the text. Problem # 2 . Solve 1.2.2 Problem # 3 . An experiment consists of a single roll of a die. DeFne sets (events): A = { outcome is greater than 3 } and B = { outcome is odd } . Specify: a) The sample space S . b) A B c) A B d) A - B e) A c B c Problem # 4 . The di±erence set operation: a) Does A - B = A - C imply that B = C ? Justify. b) Consider the set (
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Unformatted text preview: A-B )-C . Is it the same as any of the following sets: A-( B-C ), ( A-C )-B , or A-( B ∪ C )? Justify. Problem # 5 . Use the associative, distributive, De Morgan, or other laws to show that: a) [ A ∩ ( B ∪ C )] c = ( A c ∪ B c ) ∩ ( A c ∪ C c ) b) ( A ∩ B ∩ C ) c = A c ∪ B c ∪ C c Also check the validity using Venn diagrams. Problem # 6 . Subsets: a) Given A = { a,b,c } , write out all its subsets. b) Let B be a set of N elements. Prove that it has 2 N subsets....
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## This note was uploaded on 08/08/2010 for the course ECE PROF. VOLK taught by Professor Volkanrodoplu during the Summer '10 term at UCSB.

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