$\def\d{\displaystyle} \def\course{Math 228} \newcommand{\f}[1]{\mathfrak #1} \newcommand{\s}[1]{\mathscr #1} \def\N{\mathbb N} \def\B{\mathbf{B}} \def\circleA{(-.5,0) circle (1)} \def\Z{\mathbb Z} \def\circleAlabel{(-1.5,.6) node[above]{A}} \def\Q{\mathbb Q} \def\circleB{(.5,0) circle (1)} \def\R{\mathbb R} \def\circleBlabel{(1.5,.6) node[above]{B}} \def\C{\mathbb C} \def\circleC{(0,-1) circle (1)} \def\F{\mathbb F} \def\circleClabel{(.5,-2) node[right]{C}} \def\A{\mathbb A} \def\twosetbox{(-2,-1.5) rectangle (2,1.5)} \def\X{\mathbb X} \def\threesetbox{(-2,-2.5) rectangle (2,1.5)} \def\E{\mathbb E} \def\O{\mathbb O} \def\U{\mathcal U} \def\pow{\mathcal P} \def\inv{^{-1}} \def\nrml{\triangleleft} \def\st{:} \def\~{\widetilde} \def\rem{\mathcal R} \def\sigalg{\sigma-algebra } \def\Gal{\mbox{Gal}} \def\iff{\leftrightarrow} \def\Iff{\Leftrightarrow} \def\land{\wedge} \def\And{\bigwedge} \def\entry{\entry} \def\AAnd{\d\bigwedge\mkern-18mu\bigwedge} \def\Vee{\bigvee} \def\VVee{\d\Vee\mkern-18mu\Vee} \def\imp{\rightarrow} \def\Imp{\Rightarrow} \def\Fi{\Leftarrow} \def\var{\mbox{var}} \def\Th{\mbox{Th}} \def\entry{\entry} \def\sat{\mbox{Sat}} \def\con{\mbox{Con}} \def\iffmodels{\bmodels\models} \def\dbland{\bigwedge \!\!\bigwedge} \def\dom{\mbox{dom}} \def\rng{\mbox{range}} \def\isom{\cong} \DeclareMathOperator{\wgt}{wgt} \newcommand{\vtx}[2]{node[fill,circle,inner sep=0pt, minimum size=4pt,label=#1:#2]{}} \newcommand{\va}[1]{\vtx{above}{#1}} \newcommand{\vb}[1]{\vtx{below}{#1}} \newcommand{\vr}[1]{\vtx{right}{#1}} \newcommand{\vl}[1]{\vtx{left}{#1}} \renewcommand{\v}{\vtx{above}{}} \def\circleA{(-.5,0) circle (1)} \def\circleAlabel{(-1.5,.6) node[above]{A}} \def\circleB{(.5,0) circle (1)} \def\circleBlabel{(1.5,.6) node[above]{B}} \def\circleC{(0,-1) circle (1)} \def\circleClabel{(.5,-2) node[right]{C}} \def\twosetbox{(-2,-1.4) rectangle (2,1.4)} \def\threesetbox{(-2.5,-2.4) rectangle (2.5,1.4)} \def\ansfilename{practice-answers} \def\shadowprops{{fill=black!50,shadow xshift=0.5ex,shadow yshift=0.5ex,path fading={circle with fuzzy edge 10 percent}}} \newcommand{\hexbox}[3]{ \def\x{-cos{30}*\r*#1+cos{30}*#2*\r*2} \def\y{-\r*#1-sin{30}*\r*#1} \draw (\x,\y) +(90:\r) -- +(30:\r) -- +(-30:\r) -- +(-90:\r) -- +(-150:\r) -- +(150:\r) -- cycle; \draw (\x,\y) node{#3}; } \renewcommand{\bar}{\overline} \newcommand{\card}[1]{\left| #1 \right|} \newcommand{\twoline}[2]{\begin{pmatrix}#1 \\ #2 \end{pmatrix}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&}$

# AppendixBList of Symbols

Symbol Description Location
$P, Q, R, S, \ldots$ propositional (sentential) variables Paragraph
$\wedge$ logical “and” (conjunction) Item
$\vee$ logical “or” (disjunction) Item
$\neg$ logical negation Item
$\exists$ existential quantifier Subsection
$\forall$ universal quantifier Subsection
$\emptyset$ the empty set Item
$\U$ universal set (domain of discourse) Item
$\N$ the set of natural numbers Item
$\Z$ the set of integers Item
$\Q$ the set of rational numbers Item
$\R$ the set of real numbers Item
$\pow(A)$ the power set of $A$ Item
$\{, \}$ braces, to contain set elements. Item
$\st$ “such that” Item
$\in$ “is an element of” Item
$\subseteq$ “is a subset of” Item
$\subset$ “is a proper subset of” Item
$\cap$ set intersection Item
$\cup$ set union Item
$\times$ Cartesian product Item
$\setminus$ set difference Item
$\bar{A}$ the complement of $A$ Item
$\card{A}$ cardinality (size) of $A$ Item
$A\times B$ the Cartesian product of $A$ and $B$ Paragraph
$f\inv(y)$ the complete inverse image of $y$ under $f\text{.}$ Paragraph
$\B^n$ the set of length $n$ bit strings Item
$\B^n_k$ the set of legth $n$ bit strings with weight $k\text{.}$ Item
$(a_n)_{n \in \N}$ the sequence $a_0, a_1, a_2, \ldots$ Paragraph
$T_n$ the $n$th triangular number Example 2.1.4
$F_n$ the $n$th Fibonacci number Item 2.1.3.c
$\Delta^k$ the $k$th differences of a sequence Paragraph
$P(n)$ the $n$th case we are trying to prove by induction Paragraph
$42$ the ultimate answer to life, etc. Paragraph
$\therefore$ “therefore” Paragraph
$K_n$ the complete graph on $n$ vertices Paragraph
$K_n$ the complete graph on $n$ vertices. Item
$K_{m,n}$ the complete bipartite graph of of $m$ and $n$ vertices. Item
$C_n$ the cycle on $n$ vertices Item
$P_n$ the path on $n$ vertices Item
$\chi(G)$ the chromatic number of $G$ Paragraph
$\Delta(G)$ the maximum degree in $G$ Paragraph
$\chi'(G)$ the chromatic index of $G$ Paragraph
$N(S)$ the set of neighbors of $S\text{.}$ Paragraph