\documentclass[12pt,a4paper,draft]{article} % change 'draft' to 'final' before final printing
\usepackage[T1]{fontenc} %non-English hyphenation (orddeling)
\usepackage[utf8]{inputenc} %lets you write Danish letters in the tex-file:
% remember to erase the ones you aren't using!  it depends on your editor which one you need
\usepackage[danish]{babel} %change 'danish' to 'english' if writing in English
\usepackage{amsmath,amsfonts,amssymb,amsthm} %AMS' packages for symbols, theorems etc.
\usepackage[final]{graphicx} %for including figures (\includegraphics)
\usepackage{showkeys} %shows labels/references when in draft mode (you choose between 'draft' and 'final' in \documentclass). You may want to add notref and notcite: \usepackage[notref,notcite]{showkeys}
\usepackage{mathtools}

%\bibliographystyle{alpha} %if you're using BibTeX, you set the bibliographystyle here

%\frenchspacing %tells LaTeX not to insert extra space at the end of sentences

%Below are some styles for definitions, theorems, etc. defined.
%Uncomment either the Danish or the English version to use them:

%Danish version:
\theoremstyle{plain}
\newtheorem{saetn}{S�tning}[section]
\newtheorem{prop}[saetn]{Proposition}
\newtheorem{lemma}[saetn]{Lemma}
\newtheorem{kor}[saetn]{Korollar}
\theoremstyle{definition}
\newtheorem{defi}[saetn]{Definition}
\newtheorem{bem}[saetn]{Bem�rkning}
\newtheorem{eks}[saetn]{Eksempel}
\newtheorem{obs}[saetn]{Observation}
%
%English version:
%\theoremstyle{plain}
%\newtheorem{thm}{Theorem}[section]
%\newtheorem{prop}[thm]{Proposition}
%\newtheorem{lemma}[thm]{Lemma}
%\newtheorem{cor}[thm]{Corollary}
%\theoremstyle{definition}
%\newtheorem{defi}[thm]{Definition}
%\newtheorem{rem}[thm]{Remark}
%\newtheorem{ex}[thm]{Example}
%\newtheorem{obs}[thm]{Observation}
%

%Examples of handy use of \newcommand, \renewcommand and \DeclareMathOperator.
%Uncomment to use them:
\newcommand{\N}{\mathbb N} %the natural numbers
\newcommand{\Z}{\mathbb Z} %the integers
\newcommand{\Q}{\mathbb Q} %the rational numbers
\newcommand{\R}{\mathbb R} %the real numbers
\newcommand{\C}{\mathbb C} %the complex numbers
\newcommand{\E}{\mathbb E}
\newcommand{\K}{\mathbb K}
\newcommand{\F}{\mathbb F}
\newcommand{\B}{\mathbb B}
\newcommand{\D}{\mathbb D}
\newcommand{\h}{\mathbb H}
\renewcommand{\epsilon}{\varepsilon} %so that \epsilon makes a proper epsilon
\renewcommand{\phi}{\varphi} %so that \phi makes a proper phi
%\DeclareMathOperator{\Aut}{Aut} %just as an example: $\Aut(G)$ for the automorphism group of $G$


%If you want to make diagrams with \xymatrix.  Uncomment both lines to use it:
\input xy
\xyoption{all}

%To make the title, uncomment the following three lines:
\title{TITLEN} %The title
\author{Sine Vestergård Jensen} %Your name
%\date{} %The date is optional.  Default is \today.
%You must also uncomment \maketitle (which is right after \begin{document}).

\begin{document}
\subsection*{Problem 1}
 Lad $(X, \E, \mu)$ være sandsynligheds rum, da er $\mu$ sandsynligheds mål på målrummet $(X, \E)$.

\subsubsection*{a} Lad $A,B \in \E$ være sådan at $\mu (A) = \mu (B) = 1.$ Vis at den symmetriske difference $A \triangle B$ tilhører $\E$ og vis at $ \mu (A \triangle B)=0$. \\

Da vi ved at $A,B \in \E$ må der gælde følgende