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# problems01-sol - MATH S-104 Lecture 1 In-class Problem...

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MATH S-104 Lecture 1 In-class Problem Solutions June 23, 2009 Problem 1 * : Given the following statements p , q , and r , convert English to logical form or vice-versa. p : “DATAENDFLAG is o ff q : “ERROR equals 0” r : “SUM is less than 1000” a) “DATAENDFLAG is o ff , ERROR is 0, and SUM is at least 1000” p q ¬ r b) ( ¬ p q ) r “SUM is less than 1000 and either DATAENDFLAG is on or ERROR equals 0” c) “Either DATAENDFLAG is on or it is the case that both ERROR equals 0 and SUM is less than 1000” ¬ p ( q r ) Problem 2 : Generate a logic circuit for the following Boolean expressions. For each of these problems, there are multiple correct answers. a) p ( ¬ p ¬ q ) OR AND NOT NOT p q b) ( p ¬ q ) ( ¬ p r ) OR AND NOT NOT q p r AND 1

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c) p q OR AND NOT p q AND Problem 3 * : Use De Morgan’s law to negate the following: a) “John is 6 feet tall and he weighs at least 200 pounds.” “John is not 6 feet tall or he weights less than 200 pounds.” b) “The bus was late or Tom’s watch was slow.”
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