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\begin{center}\textbf{Problem Set 6 \hspace{.7in} Foundations \hspace{.7in} Due 3/21/14} \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 $A$, $B$, $C$, and $D$, $A\subseteq B \wedge C \subseteq D \Rightarrow A \times C \subseteq B \times D$.

\item For sets $A$, $B$, $C$, and $D$, $(A\cap B) \times (C\cap D) = (A\times C) \cap (B\times D)$.

\item For sets $A$, $B$, $C$, and $D$, $(A\cup B) \times (C\cup D) = (A\times C) \cup (B\times D)$.

\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 $f:\mathbb R \rightarrow \mathbb R$ and $g: \mathbb R \rightarrow \mathbb R$ be functions, and suppose $f$ is bounded.  Then $f\circ g$ is bounded.

\item Let $f:\mathbb R \rightarrow \mathbb R$ and $g: \mathbb R \rightarrow \mathbb R$ be functions, and suppose $g$ is bounded.  Then $f\circ g$ is bounded.

\item The composition of two decreasing functions is $\line(1,0){100}$.

\end{enumerate}

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