4023s09exf

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

This preview shows pages 1–2. Sign up to view the full content.

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.)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 12/28/2011.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online