# Discrete Mathematics: An Active Approach to Mathematical Reasoning

## IndexIndex

$$r$$-permutation
edges
vertices
ancestor
of a vertex, Item
argument
quantifier
arrow diagram
arthmetic sequence
binary tree
full
binomial
binomial coefficient
Binomial Theorem
bit string
branch vertex
Cartesian product
cases
proof by
child
of a vertex, Item
choose
circuit
Euler
Hamiltonian
simple, Item
trivial
circuit-free graph
closed form
sum
closed walk, Item
codomain
relation
combination
complement
of a set
complete bipartite graph
complete graph
complete set of residues
composite
conclusion
conditional
negation of, Item
statement
congruent mod $$d$$
connected
graph
vertices
connective
biconditional, Item
conditional, Item
conjunction, Item
disjunction, Item
negation, Item
constructive proof
existential statement
proof
contrapositive, Item
proof
universal conditional
converse, Item
universal conditional
converse error
quantifier
counterexample
degree
of a vertex
DeMorgan's Laws
descendant
of a vertex, Item
difference
of sets
digraph
direct proof
directed graph
disjoint sets
divides, Item
divisible
Division Algorithm. See Quotient-Remainder Theorem
divisor, Item
domain
for a quantified statement
relation
edge
parallel
empty graph
empty set
proof
endpoints of an edge
equivalence class
equivalence relation
Euler circuit
Euler path
even integer
existential
proof of
quantifier, Item
statement, Item
universal, Item
explicit formula
by iteration
proof
explicit sequence
factor, Item
factorial
Fibonacci sequence
explicit formula
forest
function
inverse
one-to-one
onto
Fundamental Theorem of Arithmetic. See Unique Factorization Theorem
geometric sequence
geometric sum
graph
circuit
circuit-free
complete
complete bipartite
directed
path
total degree
tree
Hamiltonian circuit
height
of a tree, Item
image
incident
edge
inclusion-exclusion rule
induction
proof structure
strong
integer, Item
remainder representation
internal vertex
intersection
of sets
invalid argument
inverse
function
image
of conditional, Item
relation
inverse error
quantifier
inverse function
irrational number
isolated vertex
iteration
method of
leaf
level
of vertex, Item
logical argument
logical equivalence
logical statement
loop
mathematical induction
modular arithmetic
modus ponens
universal
modus tollens
universal
multiple, Item
multiplication rule
natural number, Item
negation
logical statement
of conditional, Item
null string
odd integer
one-to-one correspondence
one-to-one function
proof
onto function
proof
pairwise disjoint sets
parallel edges
parent
of a vertex, Item
partition
Pascal's Formula
path
permutation
pigeonhole principle
generalized
power set
predicate
preimage
premise
prime
prime factorization
standard form
probability
product
product notation
product of sets
proof
by cases
by contrapositive
by induction
direct
method of exaustion
proper subset
quantifier
existential, Item
negation
universal, Item
quotient
Quotient-Remainder Theorem
proof
range
rational number
real number, Item
recurrence relation
iteration
proof
proof of explicit formula
recursively defined sequence
reflexive, Item
proof
relation
codomain
domain
equivalence
function
reflexive
symmetric
transitive
remainder
residue
rooted tree
sequence
arithmetic
explicit
explicit formula proof
Fibonacci
geometric
index
initial term
recursive
recursive formula proof
term
set
complement
difference
disjoint
identities
intersection
pairwise disjoint
proof of equality
properties
union
universal
set roster notation
set theory
sets of sets
sibling
of a vertex, Item
simple circuit, Item
simple graph
statement
existential
universal
universal conditional
vacuously true
string
binary
strong induction
proof structure
subgraph
subset
proof technique
proper
properties
successor function
sum
closed form
summation
closed form
summation notation
symmetric, Item
proof
tautology
terminal vertex
total degree
trail, Item
transitive, Item
argument
proof
transitive closure
tree
height, Item
rooted
truth set
for a predicate
truth-table
union
of sets
Unique Factorization Theorem
universal
conditional, Item
existential, Item
quantifier, Item
statement, Item
universal conditional
contrapositive
converse
vacuously true
valid argument
variable
Venn diagram
quantified argument
vertex