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# hw2 - CS 173 Discrete Structures Fall 2011 Homework 2 This...

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CS 173: Discrete Structures, Fall 2011 Homework 2 This homework contains 5 problems worth a total of 47 points. It is due on Friday, Septem- ber 9th at 4pm. As usual, put your homework into the appropriate dropbox in the base- ment of Siebel. 1. [9 points] Truth tables (a) (3 points) Give the truth table corresponding to the following expression: ( p q ) r Include a column for the intermediate result ( p q ) . (b) (2 points) Eager Eddy from down the hall claims that ( p q ) r and p ( q r ) are logically equivalent. Disprove his claim using a concrete counter-example. That is, give specific values for p , q and r for which the two expressions produce different values. (c) (4 points) For which values of p , q , and r is the following logical expression true? ( ¬ r → ¬ q ) ( ¬ p q ) ( ¬ r p ) Give a succinct description of which combinations of input values work, rather than the whole truth table. 2. [6 points] Translating notation into English Suppose we define: C ( x ) is “x takes a potion class.” Q ( x ) is “x plays Quidditch .”

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hw2 - CS 173 Discrete Structures Fall 2011 Homework 2 This...

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