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\begin{document} %(
\baselineskip 24pt

\title{Problem Set 01}
% YOUR NAME GOES HERE under Author
\author{Your Name}
\maketitle

\begin{enumerate} %(

\item (This problem was inspired by my recent experience with the
Baltimore Parking Authority in the difficulty in obtaining a parking
pass, which made me realize the high demand and low supply for these.
That is, Federal Hill parking passes are like gold.)

In English, what is the logical consequence of the following set
of statements?
\begin{itemize} %(
\item A = ``Marc leaves something valuable on display in his car.''
\item B = ``Marc's car is parked in Federal Hill.''
\item C = ``Marc's car gets broken into.''
\item D = ``Parking passes are valuable.''
\item E = ``Marc gets a \$77 parking ticket.''
\item F = ``Marc's car has a parking pass on display in his car.''
\item G = ``Marc has to pay \$77 to fix his broken car window.''
\item $A \wedge B \implies C$
\item $B \wedge \sim F \implies E$
\item $C \implies G$
\item $D \wedge B$
\end{itemize} %)
% Answer below this line




\item (This problem was inspired by graffiti I read on a
bathroom stall several years ago, which made an analogy between Clint
Eastwood and the stall's toilet paper.)\\

Translate the following sentences {\em taken literally} into
quantified logic \\
where $Problem\lx(x, p, y\rx)$ means $x$ has problem $p$ with $y$.:
\begin{enumerate} %( 
\item ``Bob has problems with everybody.'' \\
% Answer below this line

Here's what this one should be: $\forall y \exists p Problem\lx(Bob, p, y\rx)$

\item ``Bob has no problems with everybody.''  (In the sense that Bob
doesn't have problems with anybody.) \\
% Answer below this line

\item 
``Bob has problems with nobody.'' \\
% Answer below this line

\item 
``Bob has no problems with nobody.'' \\
% Answer below this line

\item 
``Bob doesn't have no problems with nobody.'' \\
% Answer below this line

\end{enumerate} %)

\item Write the previous answer (which should have been $\sim
\forall y \exists p Problem\lx(Bob, p, y\rx)$) such that the negations
appear only within predicates (i.e., no negation appears in front of a
quantifier). \\
% Answer below this line

\item BONUS: rewrite ``Clint Eastwood is rough, he's tough, and he
don't take no crud off nobody.'' taken literally in as simplified
English as possible (i.e.\ using at most one negative).\\
% Answer below this line

\end{enumerate} %)
\end{document} %)