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\centerline{Homework 1, MORALLY Due Feb 5, DEAD-CAT DAY 7}
\newcommand{\implies}{\Rightarrow}

\newif{\ifshowsoln}
\showsolntrue % comment out to NOT show solution inside \ifshowsoln and \fi blocks.

\begin{enumerate}

\item
(10 points)
When is the first midterm (give date and time)?
When is the second midterm (give date and time)?
When is the final (give date and time)?
By when do you have to inform Professor Gasarch that
you cannot make the timeslot of the first or the second midterm?
Of the final?


\item
(30 points)
Give a Propositional Formula on four variables that has exactly
three satisfying assignments.
Give the satisfying assignments.

\item
(30 points)
\begin{itemize}
\item
Do a truth table for $(p\implies q)\implies r$. 
\item
Do a truth table for $p\implies (q\implies r)$. 
\item
Are they equivalent? If NOT then state a row where they differ.
\end{itemize}


\item
(30 points)
Show that, for all $n\ge 1$, there exists a formula that is satisfied by
exactly $n$ satisfying assignments. Give the satisfying assignments.
(This is NOT by induction. Just give
the Formula. You may use DOT DOT DOT (that is ``$\dots$") though it should be clear what you mean.)


\end{enumerate}
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