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# pset1 - EECS 310 Fall 2011 Instructor Nicole Immorlica...

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EECS 310, Fall 2011 Instructor: Nicole Immorlica Problem Set #1 Due: Sept 27, 2011 1. (15 points) Graph coloring abstraction. Describe a problem (other than the two mentioned in lecture) that can be solved using a graph coloring abstraction. Give a (small) instance of the problem, convert it to a graph, describe a coloring of your graph, and explain the implied solution. 2. (15 points) Logic. (a) (5 points) The exclusive or operation is defined as: P Q is true when exactly one of P or Q is true. Find an expression equivalent to P Q using only not ( ¬ ), and ( ), and or ( ). (b) (5 points) The operators not ( ¬ ) and and ( ) are complete in the sense that any logical statement can be expressed using only these two operators. Find an expres- sion equivalent to P ⇐⇒ Q using only not ( ¬ ) and and ( ). (c) (5 points) Rewrite ¬ ( P Q ) using only not ( ¬ ) and and ( ), distributing the negation throughout the parathenses (so that the symbol ¬ is followed directly by P or Q in your final statement).

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pset1 - EECS 310 Fall 2011 Instructor Nicole Immorlica...

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