4023s09exf

4023s09exf - Name: Final Exam Instructions. Answer each of...

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Name: Final Exam Instructions. Answer each of the questions on your own paper, and be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Put your name on each page of your paper. 1. [10 Points] Let X = f 1 ; 2 ; 3 ; 4 ; 5 ; 6 g and Y = f 0 ; 10 ; 20 ; 30 g . How many elements are there in each of the following sets. Proofs are not required. Recall that P ( S ) denotes the power set of S , that is, the set of all subsets of S . (a) P ( X ) (b) P ( X ) [ X (c) Y \ Z 10 (d) Y £ Y (e) f Functions f : X ! Y g 2. [15 Points] (a) Find the greatest common divisor d = (792 ; 882) of 792 and 882, using the Euclidean Algorithm. (b) Write d = (792 ; 882) in the form d = s ¢ 792 + t ¢ 882. (c) Find the least common multiple [792 ; 882]. 3. [12 Points] (a) What is the relationship between a and n which guarantees that [ a ] n has a multiplicative inverse in Z n ? (Just state the condition. It is not necessary to verify it.)
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This document was uploaded on 12/28/2011.

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4023s09exf - Name: Final Exam Instructions. Answer each of...

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