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Neal Whittington (whittin3)
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\textbf{CS 173: Discrete Structures, Spring 2010}
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\textbf{Homework 2}
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This homework contains 6 problems worth a total of 50 points.
It is due on Friday, February 5th at 4pm.
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\begin{enumerate}
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\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}
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\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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View Full Document\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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 Spring '08
 Erickson

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