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\Huge{Quiz 1}
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\noindent{Show \emph{all} your work. No credit is given without reasonable supporting work. There are \emph{two} sides to this quiz and all logic symbols make use of the textbook notation.}

\begin{enumerate}

\item $[2]$ (logic wks \#1) Define the \emph{propositions} $p$ and $q$ below:\\

$p$:\\
\vspace{.1in}

$q$:\\
\vspace{.1in}

\begin{enumerate}
\item $[2]$ (\S1.1 \#8) Express $p\rightarrow q$ as an English sentence.
\vspace{1in}
\item $[2]$ (\S1.3 \#7) Express $\neg (p\wedge q)$ as an English sentence.
\vspace{1in}
\end{enumerate}

\item $[4]$ (\S1.3 \#41) Find a compound proposition involving the propositional variables $p$, $q$, and $r$ that is true when exactly two of $p$, $q$, and $r$ are true and is false otherwise.  

\newpage

\item (\S1.4 \#32e) Consider the following statement, ``There is a pig that can spin spider webs and talk."
\begin{enumerate}
\item $[2]$ Express the statement above using predicates, quantifiers, and logical connectives.
\vspace{1in}
\item $[2]$ Negate part (a) so that no negation is to the left of a quantifier.
\vspace{1in}
\end{enumerate}

\item $[2]$ (9/26 lecture) Let the domain be integers between $-4$ and $3$ inclusive. Determine the truth value of $\forall x,\exists y, ( x+y>0)$.  Support your conclusions!
\vspace{1in}

\item $[4]$ (\S1.2 Ex7) Suppose you are on an island that has two kinds of inhabitants, knights, whoa lways tell the truth, and their opposites, knaves, who always lie.  You encounter two people $A$ and $B$.  What are $A$ and $B$ if $A$ says ``$B$ is a knight" and $B$ says ``The two of us are opposite types"?

\end{enumerate}
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