% If you are working from this template to just write up your own
% solutions, I'm trying to keep it simple for you and there are only a
% few places you need to edit. On line 43 there's a place where the
% phrase "YOUR NAME HERE" appears; change it to your actual
% name. Several places below there are places where the phrase "YOUR
% ANSWER HERE" appears, and directly below (or replacing) those lines
% are good places to put your answers.
%
% One important thing you need to do, however (due to the complicated
% way I use a single form to produce both the question sheets and
% solution writeups) is to make sure that you keep the word 'solution'
% in your filename, or else your answers won't be printed at all.
\documentclass[12pt]{article}
 
\usepackage[margin=0.7in,dvips]{geometry}
\usepackage{fancyhdr,lastpage}
\usepackage{amsmath,amsfonts,amsthm,amssymb}
\usepackage{tikz}
\usepackage{substr}

\usepackage{hyperref}

\IfSubStringInString{\detokenize{solution}}{\jobname}{%
  % Solutions
  \newcommand\qfill{}
  \newcommand\qpage{}
  \newcommand\qonly[1]{}
  \newcommand\answer[1]{#1}
  \newcommand\question[1]{{\em #1}}
  \newcommand\rubric[1]{}
}
{%
  % Question sheets
  \newcommand\qfill{\vfill}
  \newcommand\qpage{\newpage}
  \newcommand\qonly[1]{#1}
  \newcommand\answer[1]{}
  \newcommand\question[1]{#1}
  \newcommand\rubric[1]{}
}

\pagestyle{fancy}
\lhead{MATH 311-01}
\chead{Extra Credit Problem Set \answer{ solutions}}
\rhead{\answer{}}
\lfoot{}
\cfoot{Page \thepage\ of \pageref{LastPage}}
\rfoot{{\bf due April 25, 2017}}

\newtheorem{prop}{Proposition}

% The command below redefines \neg (the logical negation character)
% to be a big tilde, in line with the usage in the book. Comment it
% out if you prefer the more traditional negation symbol.
\renewcommand*{\neg}{\mathord{\sim}}

\begin{document}
\begin{enumerate}
\item \question{Prove that for sets $A$ and $B$, if $|A|\leq |B|$,
    then $|\mathcal P(A)|\leq|\mathcal P(B)|$}

  \answer{}

\item \question{Prove (or demonstrate with a suitable function or
    functions) that the following equalities among cardinalities are
    true; recall the interval notations $(a,b)=\{x\in\mathbb
    R:a<x<b\}$ and $[a,b]=\{x\in\mathbb R:a\leq x\leq b\}$.}

  \begin{enumerate}
  \item \question{$|(0,1)|=|[0,1]|$.}

  \answer{}

  \item \question{$|(0,1)|=\mathbb R$.}

  \answer{}

  \item \question{$|[0,1]|=|[0,1]\times[0,1]|$.}

  \answer{}
  \end{enumerate}
\end{enumerate}

\end{document}
