\documentclass[letterpaper,12pt]{article}

\usepackage{amsfonts,amssymb,amsmath,amsthm,txfonts,pxfonts,mathrsfs,fullpage,enumitem}
\usepackage{xcolor}

\pagestyle{empty}
\newcommand{\RR}{{\mathbb R}}
\begin{document} 

\begin{center}\textbf{Problem Set 1 \hspace{.7in} Set Theory \& Topology \hspace{.7in} Due 1/12/18} \end{center}

\noindent You are expected to do the following problems to a high standard (i.e., at least well enough to be published in a textbook) for full credit.  Four of these problems will be selected (by Jon) for grading, with each worth 5 points.

\begin{enumerate}

\item {[Baker 1.R.13]} The inverse of the inverse of a one-to-one onto function is the original function.

\item {[Baker 1.R.14]} Let $f:X \to Y$ be a function and let $A$ and $B$ be subsets of $Y$.  If $f^{-1}(A) = f^{-1}(B)$, then $A=B$.

\item {[Baker 1.R.15]} If $f:X \to Y$ is a function, then $f(X)=Y$.

\item {[Baker 1.R.16]} If $f:X \to Y$ is onto, then $f(X)=Y$.

\item {[Baker 1.R.17]} Inverse images of sets are only defined for one-to-one functions.

\item {[Baker 1.R.18]} If $f:X \to Y$ is a function, then $f^{-1}(Y) = X$.

\item {[Baker 1.R.19]} If $f:X \to Y$ is a function and $U$ and $V$ are subsets of $X$, then $f(U \cap V)=f(U) \cap f(V)$.

\item {[Baker 1.R.20]} If $f:X \to Y$ is a function and $U$ and $V$ are subsets of $X$, then $f(U \cap V) \subseteq f(U) \cap f(V)$.

\end{enumerate}


\end{document}