# hw11-new - CS 173 Discrete Structures Spring 2010 Homework...

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CS 173: Discrete Structures, Spring 2010 Homework 11 This homework contains 3 problems worth a total of 42 regular points and 4 bonus points. It is due on Friday, April 30th at 4pm. Put your homework in the appropriate dropbox in the Siebel basement. 1. Partial Orders [16 points] (a) Suppose that A is the set of ﬁnite non-zero length sequences of integers . E.g. 5 , 2 is an element of A . So is 3 , 4 , 3 , 3, and so is 3 , 1 , - 37 , 67 , 0 , 3. A generic element of A would be x 1 ,x 2 ,...,x n where n 1 (since each sequence contains at least one integer.) Let S be the “subsequence of” relation on A deﬁned as follows: x 1 ,...,x m S y 1 ,...,y n if and only if m n and there is an integer k such that x 1 = y k , x 2 = y k +1 , ..., x m = y k + m - 1 . Prove that S is a partial order. (b) Suppose you are given two sets, X and Y with partial orders ± X and ± Y . We deﬁne a new relation ± X × Y on X × Y (the Cartesian product of sets X and Y) such that: ( a,b ) ± X × Y ( c,d ) if and only if the following is true:

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## This note was uploaded on 11/09/2011 for the course CS 173 taught by Professor Erickson during the Spring '08 term at University of Illinois, Urbana Champaign.

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hw11-new - CS 173 Discrete Structures Spring 2010 Homework...

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