begin{exercise}
begin{enumerate}
item Show that $R$ is symmetric iff $R^{-1}subseteq R$.
item Show that $R$ is transitive iff $Rcirc Rsubseteq R$.
end{enumerate}
begin{proof}
end{proof}
end{exercise}

documentclass[11pt]{article}
input{other/packages.tex}
input{other/theoremdef.tex}

usepackage{amsthm}
usepackage{amsmath}
usepackage{amscd}
usepackage{url}
usepackage[top=1.3in, bottom=1.3in, left=1.3in, right=1.3in]{geometry}

% header and footer
pagestyle{headings}

usepackage{amssymb}
usepackage{amsfonts}
usepackage{stackrel}
usepackage{mathrsfs}
usepackage{verbatim}
usepackage{enumerate}
usepackage{hyperref}
usepackage{xy}
input xy
xyoption{all}

newtheorem{exercise}{bf Exercise}
newcommand{dom}{text{dom} }
newcommand{ran}{text{ran} }
newcommand{fld}{text{fld} }
newcommand{op}[2]{langle #1,#2rangle}
newcommand{ot}[3]{langle #1,#2,#3rangle}
newcommand{ms}[1]{mathscr{#1}}

leavevmode

documentclass{article}
usepackage{theorem} % or ntheorem
theoremstyle{break}
newtheorem{exercise}{Exercise}
begin{document}
begin{exercise}
begin{enumerate}
  item foo
  item bar
end{enumerate}
end{exercise}
end{document}

usepackage{amsthm}
newtheoremstyle{break}{3pt}{3pt}{itshape}{}{bfseries}{.}{newline}{}
theoremstyle{break}
newtheorem{exercise}{Exercise}

begin{exercise}mbox{}
begin{enumerate}
  item foo
  item bar
end{enumerate}
end{exercise}

defthmt@amsthmlistbreakhack{%
  leavevmode
  vspace{-baselineskip}%
  par
  everypar{setboxz@lastboxeverypar{}}%
}

begin{exercise}
begin{enumerate}
item[]
item Show that $R$ is symmetric iff $R^{-1}subseteq R$.
item Show that $R$ is transitive iff $Rcirc Rsubseteq R$.
end{enumerate}

begin{theorem}
  mbox{}
  begin{enumerate}
  item foo
  item bar
  end{enumerate}
end{theorem}

begin{proof}$ $newline
Proof content.
end{proof}