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hw3 questions - Cornell University Spring 2014 CS2800 hw 3...

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Cornell’University,’Spring’2014 CS2800 – hw 3 Note’that’problems’marked’*’are’slightly’harder’than’easy,’and’those’marked’**’are’potentially’ more’challenging. ’ 1. *’Let’X’be’a’set’and’let’ σ ’ be’an’operation’on’X’(ie,’it±s’a’function’from’X’ × ’ X’to’X).’For’notational’ simplicity,’write’ σ (x’,’y)’=’xy.’Suppose’further’that’ σ ’ is’commutative,’associative,’and’idempotent. .’ If’we’define’x’≤’y’iff’x’=’ σ (x’,’y),’prove’that a. ≤’is’a’partial’order’on’X.
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