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COMPUTER SCIENCE 20, SPRING 2012 \\
DISCRETE MATHEMATICS FOR COMPUTER SCIENCE\\
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Class \#11 (Review of Quantificational Logic)
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\paragraph{Homework, due in hard copy Wednesday 2/22/2012 at 10:10am}
\paragraph{This is an optional homework. If turned in, your score for HW\#8 will be the higher of your original score and your score on this homework.}
\paragraph{Please write your TF's name on your homework, and list the names of any students with whom you collaborated.}
\begin{enumerate}
\item Let the universe be the set of people. Define the predicates $O(x,y)$ to be ``$x$ is older than $y$,'' $A(x)$ to be ``$x$ is an adult,'' and $B(x)$ to be ``$x$ is a baby.'' Translate the following (nonsensical) sentences into logical expressions.
\begin{enumerate}
\item There is an oldest person.
\item Everybody is older than someone.
\item No one is older than himself.
\item All adults are older than all babies.
\item Either everyone is an adult or everyone is a baby.
\item Everyone is either an adult or a baby.
\end{enumerate}
\item Again let the universe be the set of people. Using the constants $b$ for ``my baby'' and $m$ for ``me,'' and the predicate $L(x,y)$ for ``$x$ loves $y$'' translate the sentence ``Everybody loves my baby but my baby only loves me" into logical expressions.
\end{enumerate}
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