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+#+TITLE: Assignment Six
+#+AUTHOR: Lizzy Hunt
+#+STARTUP: entitiespretty fold inlineimages
+#+LATEX_HEADER: \notindent \notga \usepackage{ dsfont } \usepackage[utf8]{inputenc}  \usepackage{amsmath} \usepackage{fontspec} \usepackage[a4paper,margin=1in,portrait]{geometry} \usepackage{fontspec} \setmonofont{DejaVu Sans Mono}
+#+LATEX:  \setlength\parindent{0pt}
+#+LATEX_COMPILER: lualatex
+#+OPTIONS: toc:nil
+
+* Question One
+\begin{verbatim}
+A  -> BcDA'
+A' -> eD | ε
+B  -> xBB'
+B' -> yD | zD | ε
+D  -> Z
+\end{verbatim}
+
+* Question Two
+\begin{verbatim}
+A  -> wA'
+A' -> xA' | yA' | ε
+\end{verbatim}
+
+* Question Three
+\begin{verbatim}
+A  -> wA' | yzA'
+A' -> xA' | ε
+\end{verbatim}
+
+* Question Four
+\begin{verbatim}
+A  -> Bx
+B  -> Cy | Dz
+C  -> Awp | z
+D  -> t
+
+For i = 1, there is no immediate left recursion
+
+When i = 2 there is also no immediate left recursion
+
+When i = 3 we substituted A in C:
+
+A  -> Bx
+B  -> Cy | Dz
+C  -> Bxwp | z
+D  -> t
+
+Then B:
+A  -> Bx
+B  -> Cy | Dz
+C  -> Cyxwp | Dzxwp | z
+D  -> t
+
+And remove the immediate left recursion in C:
+A  -> Bx
+B  -> Cy | Dz
+C  -> Dzxwp | zC'
+C' -> yxwpC' | ε
+D  -> t
+
+When i = 4, there's no left recursion
+
+\end{verbatim}
+
+* Question Five
+\begin{verbatim}
+A  -> Bx | Cy
+B  -> Cz
+C  -> Bw | v
+
+When i = 1, no immediate left recursion
+
+When i = 2, no immediate left recursion
+
+When i = 3, we substitute B in C
+
+A  -> Bx | Cy
+B  -> Cz
+C  -> Czw | v
+
+, which we remove the immediate left recursion from
+
+A  -> Bx | Cy
+B  -> Cz
+C  -> vC'
+C' -> zwC' | ε
+\end{verbatim}
+
+* Question Six
+\begin{verbatim}
+first(A)  = first(B) \ ε U first(x) U first(y) = {t, w, u, x, y}
+first(B)  = first(C) U first(u) U {ε} = {t, w, u, ε}
+first(C)  = first(t) U first(w) = {t, w}
+
+follow(A) = {$} U follow(B) = {$, x}
+follow(B) = {x}
+follow(C) = follow(A) U {z} = {$, x, z}
+\end{verbatim}
+
+* Question Seven
+\begin{verbatim}
+first(A)  = first(C) = first(E) = {x, z}
+first(B)  = first(a) U {ε} = {a, ε}
+first(C)  = first(E) = {x, z}
+first(D)  = first(b) U {ε} = {b, ε}
+first(E)  = first(x) U first(z) = {x, z}
+
+follow(A) = {$} U first(y) = {$, y}
+follow(B) = follow(A) = {$, y}
+follow(C) = first(B) \ ε U follow(B)= {a, $, y}
+follow(D) = follow(C) = {a, $, y}
+follow(E) = first(D) \ ε U follow(D) = {b, a, $, y}
+\end{verbatim}