# hw2ANSWERS - \documentclass[12pt]cfw_article \textwidth =...

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\documentclass[12pt]{article} \textwidth = 6.5 in \textheight = 9 in \oddsidemargin = 0.0 in \evensidemargin = 0.0 in \topmargin = 0.2 in \headheight = 0.0 in \headsep = 0.0 in \parskip = 0.2in \parindent = 0.0in \usepackage{amsmath,amssymb,enumerate} % ========================================================= \begin{document} Neal Whittington (whittin3) \begin{center} {\LARGE \textbf{CS 173: Discrete Structures, Spring 2010} \\ \textbf{Homework 2} \\[1ex]} \end{center} This homework contains 6 problems worth a total of 50 points. It is due on Friday, February 5th at 4pm. \bigskip\hrule \begin{enumerate} %---------------------------------------------------------------------- \item \textbf{[9 points] Logic notation} Translate the following sentences into propositional or predicate logic. \begin{enumerate} \item For every cookie that contains lots of butter, that cookie is tasty and also fattening. \\ $\forall x \in C, B(x) \rightarrow (T(x) \wedge F(x))$ \\ C is the set of all cookies \\ B(x) means x contains lots of butter \\ T(x) means x is tasty \\ F(x) means x is also fattening \item Either the tablecloth is pink, or the tablecloth is white and the red light is shining on it. \\ $(P \vee W) \wedge R$ \\ P means the tablecloth is pink \\ W means the tablecloth is white \\ R means the red light is shining on it \item There exists an integer, x, that is equal to its own negation. \\ $\exists x \mathbb{Z}, x = \neg x$ \end{enumerate} %---------------------------------------------------------------------- \item \textbf{[6 points] Translating notation into English} Suppose we define: \begin{itemize} \item{} $C(x)$ is x likes to cook.''

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\item{} $B(x)$ is x plays banjo.'' \item{} $T(x)$ is x is on the CS 173 course staff.'' \item{} $A(x)$ is x is taking CS 232.'' \item{} $S$ is the set of all students. \end{itemize}
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## hw2ANSWERS - \documentclass[12pt]cfw_article \textwidth =...

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