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Name Math 45 Final Examination Fall, 2016 Prof. Silverstone Please show sufficient work to justify your answer. You may leave your answer in any valid mathematical form, unless otherwise directed. A- (1,5,10,17,20 B={ x E U I n is divisible by 5 } C-(2,4,6,8 Find: a) n( A) a) b) c) 2. Given the set S- ta,b,c,d,e,f,g,h) a) How many subsets does S have? b) How many subsets have exactly 5 elements? c) A subset is randomly chosen for the collection of all possible a) b) subsets. What is the probability that it contains exactly 3 elements? d) A subset is chosen at random from all the subsets. What is the probability that it contains the element d) a? 3. Prove the following argument by the indireet method: P→Q SR WAS
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