4023f10ex2

# 4023f10ex2 - Name Exam 2 Instructions Answer each of the...

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Name: 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: Z is the group of integers under addition; Z n is the group of congruence classes modulo n under addition of congruence classes; Z / n is the group of invertible congruence classes modulo n under multiplication of congruence classes; S n is the group of permutations of the set f 1 ; :::; n g under composition of permutations; D n is the group of symmetries of the regular n -sided polygon, with the group operation being composition of functions. 1. [12 Points] Let X = f 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9 ; 10 ; 11 ; 12 g , and let R be the relation \divides" on X . That is aRb () a j b . Then R is a partial order on X . You do not need to verify that R is a partial order. Draw the Hasse diagram for this partial order on X .

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4023f10ex2 - Name Exam 2 Instructions Answer each of the...

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