\documentclass[12pt]{article} \usepackage[letterpaper, margin=0.5in]{geometry} \geometry{letterpaper} \usepackage[parfill]{parskip} \usepackage{framed} \usepackage{graphicx} \usepackage{amsmath} \usepackage{amssymb} \usepackage{qtree} \usepackage{makecell} \usepackage{lmodern} \renewcommand*\familydefault{\sfdefault} \usepackage{tikz} \usetikzlibrary{matrix} \usepackage{mathtools} \DeclarePairedDelimiter\ceil{\lceil}{\rceil} \DeclarePairedDelimiter\floor{\lfloor}{\rfloor} \DeclarePairedDelimiter\abs{\lvert}{\rvert}% \DeclarePairedDelimiter\norm{\lVert}{\rVert}% % \abs & \norm resizes brackets, starred version doesn’t \makeatletter \let\oldabs\abs \def\abs{\@ifstar{\oldabs}{\oldabs*}} % \let\oldnorm\norm \def\norm{\@ifstar{\oldnorm}{\oldnorm*}} \makeatother \newcommand\graytag[1]{\text{\textsl{\color{gray}{#1}}}} \newcommand\tab[1][0.5cm]{\hspace*{#1}} \newcommand\imp{\rightarrow} \newcommand\thfr{\tab \therefore \tab} \newcommand\sameas{\tab \equiv \tab} \title{CSC263 – Week 3, Lecture 1} \author{Cristyn Howard} \date{Monday, January