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pset1last year

pset1last year - EECS 310 Fall 2010 Instructor Nicole...

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EECS 310, Fall 2010 Instructor: Nicole Immorlica Problem Set #1 Due: Sept 30, 2010 1. (20 points) Logic When asked to write statements in mathematical notation in this question, please do so in the most simple form (i.e., do not use paranthesis). (a) (8 points) Consider the following statement: It is a truth universally acknowledged, that “a single man in possession of a good fortune must be in want of a wife.” Let P be the proposition “A single man is in possession of a good fortune” and Q be the proposition “A single man wants a wife”. 1. Rewrite this statement (i.e., the portion of the statement in quotes) in mathe- matical notation using the defined propositions P and Q and the logical oper- ators , , , , and/or ¬ . 2. Describe someone that disproves the statement. Be sure to explain why it’s a counterexample. 3. Write the converse of the statement in both mathematical notation using the defined proposition P and Q and the logical operators , , , , and/or ¬ and English.

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