$\def\d{\displaystyle} \def\course{Math 228} \newcommand{\f}{\mathfrak #1} \newcommand{\s}{\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}{node[fill,circle,inner sep=0pt, minimum size=4pt,label=#1:#2]{}} \newcommand{\va}{\vtx{above}{#1}} \newcommand{\vb}{\vtx{below}{#1}} \newcommand{\vr}{\vtx{right}{#1}} \newcommand{\vl}{\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}{ \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}{\left| #1 \right|} \newcommand{\twoline}{\begin{pmatrix}#1 \\ #2 \end{pmatrix}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&}$

# IndexIndex

$\Delta^k$-constant
antecedent
argument
arithmetic sequence
biconditional, Item
bijection
binomial coefficients
binomial identity
bipartite
bit string
bow ties
Brooks' Theorem
cardinality
Cartesian product
cases
characteristic equation
characteristic roots
chromatic index
chromatic number
clique
closed formula
codomain
coloring
combination
complement
complete graph
composition
conclusion
conditional, Item
congruence
conjunction, Item
connected
connectives
and, Item
if and only if, Item
implies, Item
not, Item
or, Item
consequent
contrapositive, Item
proof by
converse, Item
convex
counterexample
cube
cycle, Item
De Morgan's laws
deduction rule
degree, Item
derangement
difference, of sets
Diophantine equation
direct proof
disjoint
disjunction, Item
divides
divisibility relation
Division algorithm
Doctor Who
dodecahedron
domain
double negation
edges
empty set, Item
Euler path, Item
Euler's formula
existential quantifier
faces
factorial
Fibonacci sequence
finite differences
Four Color Theorem
function
gcd
geometric sequence
girth
Goldbach conjecture
graph, Item
greatest commond divisor
Hall's Marriage Theorem
Hamilton path
Hanoi
hypothesis
icosahedron
if and only if, Item
if…, then…, Item
implication, Item
inclusive or
induced subgraph
induction
strong induction
inductive hypothesis, Item
injection
integers
intersection
inverse image
isomorphic
isomorphism
isomorphism class
iteration
k-permutation
Königsberg
lattice path
law of logic
logical equivalence
logically valid, seelaw of logic
magic chocolate bunnies
matching
matching condition
mod
modular arithmetic
modulo $n$
modus ponens
monochromatic
multigraph
multiplicative principle
natural numbers, Item
necessary condition
negation, Item
neighbors
NP-complete
octahedron
one-to-one
onto
partial sums
Pascal's triangle
perfect graph
permutation
Petersen graph
PIE
Pigeonhole principle
planar
Platonic solids
polyhedron
polynomial fitting
power set
premises
prime numbers
principle of inclusion/exclusion
product notation
proof by cases
proof by contrapositive
proposition
quantifiers
exists
for all
Ramsey theory
range
rationals, Item
reals, Item
recurrence relation
recursive definition
reference, self, seeself reference
self reference, seereference, self
sequence
set
set difference
Sigma notation
stars and bars
statement
subgraph
induced
subset
sufficient condition
summation notation
surjection
tautology
telescoping
tetrahedron
Tower of Hanoi
tree, Item
triangular numbers
truth table
truth value
union
universal quantifier
valid
Venn diagram
vertex coloring
vertices
Vizing's Theorem
walk, Item
weight, of a string, Item
word