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\section*{CS 70 homework 1 solutions}
Your full name: PUT YOUR NAME HERE
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Your login name: PUT YOUR LOGIN NAME HERE
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Homework 1
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Your section number: PUT YOUR SECTION NUMBER HERE
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Your list of partners: LIST YOUR PARTNERS HERE
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\begin{enumerate}
\item
\begin{enumerate}
\item Read the course web page.
Write on your homework, immediately after your name, the following sentence:
``I understand and will comply with the
academic integrity policy.''
YOUR ANSWER GOES HERE.
\item What is David Wagner's favorite number?
The answer is found on the course newsgroup, \texttt{ucb.class.cs70}.
Look for the post from David Wagner titled ``The answer to question 1(b),''
and write down the answer you find there.
Instructions on how to access the newsgroup
may be found on the course web page.
(Why are we having you do this? The class newsgroup is your best source
for recent announcements, clarifications on homeworks, and related matters,
and we want you to be familiar with how to read the newsgroup.)
YOUR ANSWER GOES HERE.
\end{enumerate}
\item
For each of the following, define proposition
symbols for each simple proposition in the argument (for example, $P$ =
``I will ace this homework''). Then write out the logical form of
the argument. If the argument form corresponds to a known inference
rule, say which it is. If not, show that the proof is correct using
truth tables.
\begin{enumerate}
\item I will ace this homework and I will have fun doing it.
Therefore, I will ace this homework.
YOUR ANSWER GOES HERE.
\item It is hotter than 100 degrees today or the pollution is
dangerous. It is less than 100 degrees today. Therefore, the pollution
is dangerous.
YOUR ANSWER GOES HERE.
\item Tina will join a startup next year. Therefore,
Tina will join a startup next year or she will be unemployed.
YOUR ANSWER GOES HERE.
\item If I work all night on this homework, I will answer all the
exercises. If I answer all the exercises, I will understand the
material. Therefore, if I work all night on this homework, I will
understand the material.
YOUR ANSWER GOES HERE.
\end{enumerate}
\item
Recall that $\N=\{0,1,\ldots\}$ denotes the set of natural numbers,
and $\Z=\{\ldots,-1,0,1,\ldots\}$ denotes the set of integers.
\begin{enumerate}
\item Define $P(n)$ by
\[ P(n) = \forall m \in \N . \; m