\documentstyle[marc,12pt,24.151-ps]{article}
\setallmargins{1.25in}
\pagestyle{empty}
\def\prob #1.{\item[(#1)]}
\def\a{$\alpha$}
\def\t{$\iota$}
\def\n{$\neg$}

\def\impl{$\rightarrow$}
\def\iff{$\leftrightarrow$}

\def\E{$\exists$}
\def\A{$\forall$}
\def\and{$\wedge$}

\catcode`E=\active
\catcode`A=\active
\catcode`\&=\active

\let E\E
\let A\A
\let &\and
\begin{document}
\head{April 2, 1992}

\begin{enumerate}
\prob 1.
W(\t x)Pxm \\
(Ex)((Ay)(Pym \iff{} y=x) & Wx)

\prob 2.
I(\t x)Pxm w \\
(Ex)((Ay)(Pym \iff{} y=x) & Ixw)

\prob 3.
M(\t x)Pxm (\t y)Pyh \\
(Ew)((Ax)(Pxm \iff{} x=w) & Mw(\t y)Pyh) \\
(Ew)((Ax)(Pxm \iff{} x=w) & (Ey)((Az)(Pzh \iff{} z=y) Mwy))

\prob 4.
\n(\char69!x)(\t x)Pxc \\
\n(Ex)(Ay)(Pyc \iff{} y=x)

\prob 5.
\n(\t x)Pxm = (\t y)Pyh) \\
(Ew)((Ax)(Pxm \iff{} x=w) & (Ey)((Az)(Pzh \iff{} z=y) w=y))

\prob 6.
\n P(\t x)Pxm h \\
\n (Ex)((Ay)(Pym \iff{} y=x) & Pxh)

\prob 7.
I(\t x)Pxm w \impl{} W(\t x)Pxm \\
(Ex)((Ay)(Pym \iff{} y=x) & Ixw) \impl{} (Ex)((Ay)(Pyh \iff{} y=x) & Wx)

\end{enumerate}
\end{document}
