hwk139_1-S11

# hwk139_1-S11 - A B-C A-C-B or A B ∪ C Justify Problem 3...

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UNIVERSITY OF CALIFORNIA, SANTA BARBARA Department of Electrical and Computer Engineering ECE 139 Probability and Statistics Spring 2011 Homework Assignment #1 (Due on Tuesday 4/5/2011 by 8 pm in the Homework Box ) Please indicate whether you are Sophomore, Junior or Senior, and EE vs CE or other. This will only be used for statistical analysis of background/preparation diversity in the class. Problem # 1 . Consider a single roll of a die. Deﬁne sets (events): A = { outcome is 3 } and B = { outcome is odd } . Specify: a) The sample space S (the set of all outcomes). b) A B c) A B d) A - B e) A c B c Problem # 2 . A closer look at the diﬀerence set operation: a) Does A - B = A - C imply that B = C ? Justify. b) Consider the set ( A - B ) - C . Is it the same as any of the following sets:

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Unformatted text preview: A-( B-C ), ( A-C )-B , or A-( B ∪ C )? Justify. Problem # 3 . 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 # 4 . Subsets challenge: 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. c) Let C be a subset of B containing k elements ( k < n ). How many subsets does B have, which are mutually exclusive with C ? Problems # 5, 6 : Solve 1.8.1, 1.8.2 in the text....
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hwk139_1-S11 - A B-C A-C-B or A B ∪ C Justify Problem 3...

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