MI
~:
List of
Symbols
Subject
Symbol
Meaning
Page
Logic
not
p
3
pAq
pandq
3
pvq
porq
3
p
E
q
or
p
XOR
q
p
or
q
but
not both
p
and
q
7
P
Q
P
is
logically
equivalent
to
Q
8
p
q
if
pthenq
18
p
q
p
if
and
only
if
q
24
therefore
29
P(x)
predicate
in
x
76
P(x)
=t-
Q(x)
every
element
in
the
truth
set
for
P
(x)
is
in
84
the truth set
for
Q(x)
P(x)
<>
Q
(x
P(x)
and
Q(x)
have
identical
truth sets
84
V
for
all
78
A
there exists
79
Applications
of
Logic
N
NOT-gate
46
AND-gate
46
ROR-gate
46
NAND
NAND-gate
54
NOR-gate
54
Sheffer
stroke
54
4
Peirce
arrow
54
r2
number
written
in
binary notation
58
nOo
number written
in
decimal
notation
58
n16
number
written
in
hexadecimal notation
71
Number
d
I
n
d
divides
n
148
Theory
and d%
n
d
does
not
divide
n 149
Applications
n
div
d
the
integer quotient
of
n
divided by
d
158
n
mod
d
the
remainder
of
n
divided
by
d
158
[xj
the
floor
of
x
165
Fxl
the
ceiling
of
x
165
W the
absolute
value
of
x
164
gcd(a,
b)
the
greatest
common
divisor
of
a
and
b
192
x
:=
e
x
is
assigned
the value
e
186
Subject
Symbol
Meaning
Page
Sequences
...
and
so
forth
199
n
E
ak
the
summation
from
k
equals
m
to n
of
ak
202
k=m
n
fl
-k
the
product
from
k
equals
m
to
n
of
a,
205
k=m
n&
n
factorial
206
a
E
A
a
0
A
a
is
an
element
of
A
a
is
not
an
element
of
A
76
76
(a,,
a
2
, ... ,
a.)
Ix
E
D I Plx)}
R,
R-,
R+,
Ronneg
Z'
Z-'
Z+
znonneg
Q,
Q-
Q+,
Qnonneg
N
A
C
B
A
g
B
A=B
A
=B
A
U
B
A
n B
A'
(xby)
(XI,
X29
* * * ,
Xn)
A
x
B
A,
x A
2
x..
X
An
0
97(A)
the
set
with
elements
a,,
a
2
, ...,
an
the
set
of
all
x
in
D
for
which
P(x)
is
true
the
sets
of
all
real
numbers, negative
real
numbers, positive
real
numbers,
and
nonnegative
real
numbers
the sets
of
all
integers,
negative
integers,
positive
integers,
and
nonnegative
integers
the
sets
of
all
rational numbers, negative
rational numbers,
positive
rational
numbers,
and
nonnegative rational numbers
the
set
of
natural
numbers
A
is
a
subset
of
B
A
is
not
a
subset
of
B
A
equals
B
A
union
B
A
intersect
B
the
difference
of
B
minus
A
the
complement
of
A
ordered
pair
ordered
n-tuple
the
Cartesian
product
of
A
and
B
the
Cartesian
product
of
Al,
A
2 .
A,
the
empty
set
the
power
set
of
A
Set
Theory
76
77
76,
77
76,
77
76,
77
77
256
257
258
260
260
260
260
264
264
265
265
262
264
List
of
Symbols
Subject
Symbol
Meaning
Page
Counting
and
N
(A)
the
number
of
elements
in
a
set
A
299
Probability
P(A)
the
probability
of
a set
A
299
P(n,
r)
the
number
of
r-permutations
of
a set
of
315
n
elements
(n)
n
choose
r,
the
number
of
r-combinations
334
r
of
a
set
of
n
elements,
the number
of
r-element
subsets
of
a
set
of
n
elements
[x,
1
,
Xi2
i
....
X
I
multiset
of
size
r
349
P(A
I
B)
the
probability
of
A
given
B
376
Functions
f:
X
-+ Y
f
is
a
function
from
X
to
Y
390
f
(x)
the
value
of f
at
x
390
x-f|y
f
sends
x
to
y
390
f
(A)
the image
of
A
402
f 1
(C)
the
inverse
image
of C
402
ix
the
identity function on
X
394
bx
b
raised
to
the
power
x
411
expb
(x)
b raised
to
the
power x
411
1ogb
(x)
logarithm
with base
b
of
x
395
F-1
the inverse
function
of
F
415
f
og
the
composition of g
and
f
432
Algorithm
x
- y
x
is
approximately
equal
to
y
206
Efficiency
O(f
(x))
big-0
of
f
of
x
519
(f
(x))
big-Omega
of f
of
x
519
J(f
(x))
big-Theta
of
f
of
x
519
Relations x
R
y
x
is
related
to
y
by
R
572
R
the
inverse relation
of
R 578
m
=
n
(mod
d)
m
is
congruent
to
n
modulo
d
597
[a]
the
equivalence class
of a
599
x
-<
y
x
is
related
to
y
by
a partial order relation
<
635
Continued
on
first
page
of
back
endpapers.
DISCRETE
MATHEMATICS
WITH
APPLICATIONS
THIRD
EDITION
SUSANNI
DePaul
U
k
S.
EPP
university
TF-IcHIVIScON
BROOKS/COLE
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