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\begin{center}\textbf{Problem Set 6 \hspace{.7in} Foundations \hspace{.7in} Due 3/14/18} \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 For sets $A$ and $B$, $(A \cap B)' = A' \cup B'$.

\item  For sets $A$ and $B$, $(A \cup B)' = A' \cap B'$.

\item If $j \in I$, then $A_j \subseteq \bigcup_{i \in I} A_i$. 

\item If $j \in I$, then $\bigcap_{i \in I} A_i \subseteq A_j$. 

\item Let $f$ and $g$ be bounded functions, both with domain $D$.  Then $f+g$ is a bounded function.

\item Let $f$ and $g$ be bounded functions, both with domain $D$.  Then $f-g$ is a bounded function.

\item Let $f$ and $g$ be bounded functions, both with domain $D$.  Then $f \cdot g$ is a bounded function.

\item Let $f$ and $g$ be bounded functions, both with domain $D$.  Then $f/g$ is a bounded function.

\item If $f:\mathbb{R} \to \mathbb{R}$ and $g:\mathbb{R} \to \mathbb{R}$ are strictly increasing, then $f+g$ is strictly increasing.

\item If $f:\mathbb{R} \to \mathbb{R}$ and $g:\mathbb{R} \to \mathbb{R}$ are odd functions, then $f-g$ is odd.

\end{enumerate}

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