diff --git a/eulerg/eulerg.tex b/eulerg/eulerg.tex
index 94dc128..393db18 100644
--- a/eulerg/eulerg.tex
+++ b/eulerg/eulerg.tex
@@ -107,8 +107,8 @@ in the $A$, $B$ case
 $ A \backslash B = \emptyset \wedge B \backslash A \neq \emptyset $
 This is not the case for $D$, $E$ where:
 $ D \backslash E \neq \emptyset \wedge E \backslash D \neq \emptyset $.
-Another way of expressing this is that $A \cap B \neq \emptyset$ and 
-$ D \subset E$.
+Another way of expressing this is that $D \cap E \neq \emptyset$ and 
+$ A \subset B$.
 
 \paragraph{Enclosure}
 To distinguish between these we can term the $A$, $B$ case to be 
@@ -158,7 +158,7 @@ $$ B {\enc} A \wedge A {\enc} C \implies B {\enc} C $$
 Enlcosure relationships are transitive
 \end{definition}
 
-\section{Representing Euler Diagrams as sets of relationships}
+\section{Representing Euler Diagrams \\ as sets of relationships}
 
 The diagram in figure \ref{fig:eulerg1} can be represented by the following relationships.
 
@@ -264,7 +264,7 @@ enclosing $PIC1$. Figure \ref{fig:eulerg_pic_g_a}
 shows contour A enclosing all elements in $PIC1$
 
 \pagebreak[0]
-\subsection{Enclosure and pure intersection in the graph}
+\subsection{Enclosure and pure \\ intersection in the graph}
 \begin{figure}[h]
  \centering
  \includegraphics[width=200pt,bb=0 0 330 162,keepaspectratio=true]{./eulerg/eulerg_pic_g_a.jpg}
@@ -289,7 +289,7 @@ see figure \ref{fig:eulerg_pic_g_a_unc}.
 
 
 \pagebreak[0]
-\section{Reduction of searches for available zones}
+\section{Reduction of searches \\ for available zones}
 
 Another property of any {\pic} $P$, is that
 the maximum number of euler zones within it is 
@@ -322,7 +322,7 @@ by any other contours. A brute force search for available zones using area opera
 is therefore of the order $N.2^N$ (where N is the number of contours in the diagram).
 By using the result in definition \ref{picreduction}, we can break the diagram into small segments
 (the {\pic}s) which have an order $|P|.2^{|P|}$.
-The order of area operations is generally\footnote{In the case where the diagram is not comprised of just one {\pic}, which has no enclosing contours} 
+The order of area operations is generally\footnote{In the case where the diagram is not comprised of just one {\pic}, which has no enclosing contours.} 
 reduced  by requiring several  $|P|.2^{|P|}$
 instead of $N.2^N$ as $P \leq N$.