deletions | additions       diff --git a/Ex3.b.tex b/Ex3.b.tex  new file mode 100644  index 0000000..794deaf  --- /dev/null  +++ b/Ex3.b.tex 
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\newcommand{\empty}{\varnothing}  \newcommand{\wp}[2]{wp\left(#1, #2\right)}  \newcommand{\if}[2]{if\left(#1\right) \ \{ #2 \}}  \newcommand{\else}[1]{else \ \{ #1 \}}  \newcommand{\ie}[3]{\if{#1}{#2} \ \else{#3}}  \newcommand{\a}[0]{\ \land \ }  \newcommand{\mtt}[1]{\text{#1}}  \newcommand{\mbb}[1]{\mathbf{#1}}  \newcommand{\T}[0]{\mbb{\top}}  \newcommand{\F}[0]{\mbb{\bot}}  \newcommand{\rule}[1]{\ (\mbb{§#1})}  \section{Ex3.b}  Given:  \begin{equation}  \begin{split}  R &= big > small  \end{split}  \end{equation}  Then:  \begin{equation}  \begin{split}  & \wp{\ie{x > y}{big, small := x, y}{big, small := y, x}}{R} \\  \rule{4} \iff & (x > y \to \wp{big, small := x, y}{R}) \a (x \leq y \to \wp{big, small := y, x}{R})\\  \rule{1} \iff & (x > y \to x > y) \a (x \leq y \to x < y)\\  \iff & x \leq y \to x < y \\  \end{split}  \end{equation}  This is not true for all $x, y \in \mathbb{Z}$, specifically when $x = y$.  Therefore:  \begin{equation}  \begin{split}Q &= x \neq y\\  \end{split}  \end{equation}