diff --git a/component_failure_modes_definition/component_failure_modes_definition.tex b/component_failure_modes_definition/component_failure_modes_definition.tex
index 9f01bf9..cbb2c12 100644
--- a/component_failure_modes_definition/component_failure_modes_definition.tex
+++ b/component_failure_modes_definition/component_failure_modes_definition.tex
@@ -309,8 +309,9 @@ It is an implied requirement of EN298 for instance to consider double simultaneo
 To generalise, we may need to consider $N$ simultaneous 
 failure modes when analysing a functional group. This involves finding
 all combinations of failures modes of size $N$ and less.
-The Powerset concept from Set theory when applied to a set S is the set of all subsets of S, including the empty set 
-\footnote{The empty set is a special case for FMMD analysis, it simply means there
+The Powerset concept from Set theory is useful model this.
+The powerset, when applied to a set S is the set of all subsets of S, including the empty set 
+\footnote{The empty set ( $\emptyset$ ) is a special case for FMMD analysis, it simply means there
 is no fault active in the functional~group under analysis}
 and S itself.
 In order to consider combinations for the set S where the number of elements in each sub-set of S is $N$ or less, a concept of the `cardinality constrained powerset'
@@ -326,7 +327,7 @@ Consider the set $S = \{a,b,c\}$.
 
 The powerset of S: 
 
-$$ \mathcal{P} S = \{ 0, \{a,b,c\}, \{a,b\},\{b,c\},\{c,a\},\{a\},\{b\},\{c\} \} $$
+$$ \mathcal{P} S = \{ \emptyset, \{a,b,c\}, \{a,b\},\{b,c\},\{c,a\},\{a\},\{b\},\{c\} \} $$
 
 
 $\mathcal{P}_{2} S $ means all subsets of S where the cardinality of the subsets is 
@@ -366,14 +367,15 @@ from $1$ to $cc$ thus
 
 \subsection{Actual Number of combinations to check \\ with Unitary State Fault mode sets}
 
-Where all components analysed only have one fault mode, the cardinality constrained powerset
-calculation give the correct number of test case combinations to check.
-Because  set of failure modes is constrained to be unitary state, the acual number will
-be less.
-
-
-What must actually be done is to subtract the number of component `internal combinations'
-from the cardinality constrain powerset number.
+Where all the fault modes in $S$ were to be independent,
+the cardinality constrained powerset
+calculation (in equation \ref {eqn:ccps}) would give the correct number of test case combinations to check.
+Because  sets of failure modes in FMMD analysis are constrained to be unitary state,
+the actual number of test cases to check will usually 
+be less than this. This is because combinations of faults with a components failure mode set
+are impossible under the conditions of a unitary state failure mode set.
+To correct equation \ref{eqn:ccps} we must subtract the number of component `internal combinations'
+for each component in the functional group under analysis.
 
 \subsubsection{Example: Two Component functional group \\ cardinality Constraint of 2}
 
@@ -388,38 +390,17 @@ applying equation \ref{eqn:ccps} gives :-
 
 $$\frac{5!}{1!(5-1)!} + \frac{5!}{2!(5-2)!}  = 15$$
 
-This is composed of ${1 \choose 5}$
-five single fault modes, and ${2 \choose 5}$ ten double fault modes.
+This is composed of ${5 \choose 1}$
+five single fault modes, and ${5 \choose 2}$ ten double fault modes.
 However we know that the faults are mutually exclusive for a component.
 We must then subtract the number of `internal' component fault combinations for each component in the functional~group.
 For component R there is only one internal component fault that cannot exist
 $R_o \wedge R_s$. As a combination ${2 \choose 2} = 1$ . For $T$ the component with 
-  three  fault modes ${2 \choose 3} = 3$.
+  three  fault modes ${3 \choose 2} = 3$.
 Thus for $cc == 2$, under the conditions of unitary state failure modes in the components $R$ and $T$, we must subtract $(3+1)$.
 The number of combinations to check is thus 11, $|\mathcal{P}_{2}(FG_cfg)| = 11$, for this example and this can be verified
 by listing all the required combinations:
-%
-%\vbox{
-%\subsubsection{All Eleven Cardinality Constrained \\ Powerset of 2 Elements Listed}
-%%\tiny
-%\begin{enumerate}
-%\item $\{R_o T_o\}$
-%\item $\{R_o T_s\}$
-%\item $\{R_o T_h\}$
-%\item $\{R_s T_o\}$
-%\item $\{R_s T_s\}$
-%\item $\{R_s T_h\}$
-%\item $\{R_o \}$
-%\item $\{R_s \}$
-%\item $\{T_o \}$
-%\item $\{T_s \}$
-%\item $\{T_h \}$
-%\end{enumerate}
-%%\normalsize
-%}
-%
 
-%$$ |\mathcal{P}_{2}(FG_cfg)| = 11 $$
 
 
 $$ \mathcal{P}_{2}(FG_cfg) =  \{
@@ -433,21 +414,33 @@ $$
 \{
     \{R_o T_o\}, \{R_o T_s\}, \{R_o T_h\}, \{R_s T_o\}, \{R_s T_s\}, \{R_s T_h\}, \{R_o \}, \{R_s \}, \{T_o \}, \{T_s \}, \{T_h \}
 \}
-| = 11 $$
+| = 11 
+$$
 
 
 \subsubsection{Establishing Formulae for unitary state failure mode \\
 cardinality calculation}
 
-The cardinality constrained powerset equation \ref{eqn:ccps} corrected for 
-unitary state failure modes can be 
-written as a general formula (see equation \ref{eqn:correctedccps}), where C is a set of the components (indexed by j where J 
-is the set of components  in the functional~group under analyis) and $|{C}|$
-indicates the number of mutually exclusive fault modes each component has:-
+The cardinality constrained powerset in equation \ref{eqn:ccps} can be corrected for 
+unitary state failure modes.
+This is written as a general formula in equation \ref{eqn:correctedccps}. 
+
+%\indent{
+where :
+\begin{itemize}
+\item Let $C$ be a set of components (indexed by $j \in  J$)
+that are members of the functional group $FG$
+i.e. $ \forall j \in J | C_j \in FG $
+\item Let $|{C}_{j}|$
+indicate the number of mutually exclusive fault modes each component has
+\item Let $SU$ be a set of unitary state failure modes from the functional group
+nder analysis $SU = FM(FG)$
+\end{itemize}
+%}
+
 
-%$$ \#\mathcal{P}_{cc} S = \sum^{k}_{1..cc} \frac{\#S!}{k!(\#S-k)!}    $$
 \begin{equation}
- |{\mathcal{P}_{cc}S}| = {\sum^{k}_{1..cc}  \frac{|{S}|!}{k!(|{S}| - k)!}}  - {\sum^{j}_{j \in J} {|{C_{j}}| \choose cc}} 
+ |{\mathcal{P}_{cc}SU}| = {\sum^{k}_{1..cc}  \frac{|{SU}|!}{k!(|{SU}| - k)!}}  - {\sum^{j}_{j \in J} {|{C_{j}}| \choose cc}} 
  \label{eqn:correctedccps}
 \end{equation}
 
@@ -455,16 +448,15 @@ Expanding the combination in equation \ref{eqn:correctedccps}
 
 
 \begin{equation}
- |{\mathcal{P}_{cc}S}| = {\sum^{k}_{1..cc}  \frac{|{S}|!}{k!(|{S}| - k)!}}   - {\sum^{j}_{j \in J}   \frac{|{C_j}|!}{cc!(|{C_j}| - cc)!}}  
+ |{\mathcal{P}_{cc}SU}| = {\sum^{k}_{1..cc}  \frac{|{SU}|!}{k!(|{SU}| - k)!}}   - {\sum^{j}_{j \in J}   \frac{|{C_j}|!}{cc!(|{C_j}| - cc)!}}  
  \label{eqn:correctedccps2}
 \end{equation}
 
 Equation \ref{eqn:correctedccps2} is useful for an automated tool that
-would verify that a `N' simultaneous failures model had been completly covered.
-By knowing how many test case should be covered, and checking the cardinality
-associated with the test cases complete coverage would be confirmed.
+would verify that a `N' simultaneous failures model had complete failure mode coverage.
+By knowing how many test cases should be covered, and checking the cardinality
+associated with the test cases, complete coverage would be confirmed.
 
-%$$ \#\mathcal{P}_{cc} S = \sum^{k}_{1..cc}  \big[ \frac{\#S!}{k!(\#S-k)!}  - \sum_{j} (\#C_{j} \choose cc \big]  $$
 
 
 \section{Component Failure Modes and Statistical Sample Space}