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\begin{center}\textbf{Problem Set 2 \hspace{.7in} Foundations \hspace{.7in} Due 1/22/17} \end{center}

\noindent Four of these problems will be graded (our choice, not yours!), with each problem worth 5 points.  Clear and complete justification is required for full credit.  You are welcome to discuss these problems with anyone and everyone, but must write up your own final submission without reference to any sources other than the textbook and instructor. 

\begin{enumerate}
\item If $p | a$ and $p | b$ then $p^2 | ab$.\\
\item If $a \equiv_n 1$ and $b \equiv_n 1$, then $a \cdot b \equiv_n 1$.\\
\item If $a \equiv_n 0$ and $b \equiv_n c$, then $a + b \equiv_n c$.\\
\item If $n, a$, and $b$ and $c$ are integers for which $a \equiv_n b$, then $a + c \equiv_n b + c$.\\
\item Do the WeBWorK "Implication" assignment, available via 
\begin{center} http://crlinwebwork2.coe.edu/webwork2/MTH-215/\end{center}
\item Do the WeBWorK "Truth Tables" assignment, available via  
\begin{center} http://crlinwebwork2.coe.edu/webwork2/MTH-215/ \end{center}
\item	Score at least 6 out of 7 on the Truth Tables Gateway on WeBWorK, available via
\begin{center} http://crlinwebwork2.coe.edu/webwork2/MTH-215/quiz\_mode/TTGateway/ \end{center}
\item The statements $\neg (P \lor Q)$ and $\neg P \land \neg Q$ are logically equivalent. [DeMorgan's Law]
\item	A statement and its inverse are logically equivalent.
\item	A statement and its contrapositive are logically equivalent.
\item	The statements $P \land (Q \lor R)$ and $(P \land Q) \lor R$ are logically equivalent.
\item	The statements $P \land (Q \lor R)$ and $(P \land Q) \lor (P \land R)$ are logically equivalent.

\end{enumerate}

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