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Unformatted text preview: Name: Solutions Exam 2 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. Some useful notation: is the group of integers under addition; u1D45B is the group of congruence classes modulo u1D45B under addition of congruence classes; u1D45B is the group of invertible congruence classes modulo u1D45B under multiplication of congruence classes; u1D446 u1D45B is the group of permutations of the set { 1 , ..., u1D45B } under composition of permutations; u1D437 u1D45B is the group of symmetries of the regular u1D45Bsided polygon, with the group operation being composition of functions. 1. [12 Points] Let u1D44B = { 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } , and let u1D445 be the relation divides on u1D44B . That is u1D44Eu1D445u1D44F u1D44E u1D44F . Then u1D445 is a partial order on u1D44B . You do not need to verify that u1D445 is a partial order. Draw the Hasse diagram for this partial order on u1D44B . Solution. 8 12 4 6 9 10 2 3 5 7 11 2. [12 Points] Let u1D434 be the set of integers defined by u1D434 = { u1D45B : 11 u1D45B &lt; 13 } . Define an equivalence relation on u1D434 by the rule u1D45Bu1D445u1D45A 5 ( u1D45B u1D45A ). You do not need to verify that this is an equivalence relation. List all of the equivalence classes for u1D445 ....
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This document was uploaded on 12/28/2011.
 Fall '09

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