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hw1-solns - Illinois Institute of Technology Department of...

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Illinois Institute of Technology Department of Computer Science Solutions to Homework Assignment 1 CS 330 Discrete Structures Spring Semester, 2008 1. Page 19, Problem 28. Construct a truth table for each compound proposition. (a) p → ¬ p p ¬ p p → ¬ p F T T T F F (b) ( p q ) ( p q ) p q ( p q ) ( p q ) ( p q ) ( p q ) F F F F T F T F T T T F F T T T T T T T 2. Page 50, Problem 62. Express each of the following propositional statements. P(x) - x is a duck Q(x) - x is one of my poultry R(x) - x is an office S(x) - x is willing to waltz (a) No ducks are willing to waltz x ( P ( x ) → ¬ S ( x )) (b) No officers ever decline to waltz x ( R ( x ) S ( x )) (c) All my poultry are ducks x ( Q ( x ) P ( x )) (d) My poultry are not officers x ( Q ( x ) → ¬ R ( x )) (e) Does (d) follow from a, b, c? Yes. Ducks do not waltz (a), officers do waltz (b), therefore ducks are not officers. Since all my poultry are ducks (c), my poultry are not officers (d). 3. Page 61, Problem 32. Express the negations of each of these statements so that all negation symbols immediately precede predicates.
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