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df&&&&&&&&&&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
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List of Symbols
Subject Symbol Meaning Page
Logic ∼p not p 25
p∧q p and q 25
p∨q p or q 25
p ⊕ q or p XOR q p or q but not both p and q 28
P≡Q P is logically equivalent to Q 30
p→q if p then q 40
p↔q p if and only if q 45
∴ therefore 51
P(x) predicate in x 97
P(x) ⇒ Q(x) every element in the truth set for P(x) is in 104
the truth set for Q(x)
P(x) ⇔ Q(x) P(x) and Q(x) have identical truth sets 104
∀ for all 101
∃ there exists 103
Applications
of Logic NOT NOT-gate 67
AND AND-gate 67
OR OR-gate 67
NAND NAND-gate 75
NOR NOR-gate 75
| Sheffer stroke 74
↓ Peirce arrow 74
n2 number written in binary notation 78
n 10 number written in decimal notation 78
n 16 number written in hexadecimal notation 91
Number d |n d divides n 170
Theory and d /| n d does not divide n 172
Applications
n div d the integer quotient of n divided by d 181
n mod d the integer remainder of n divided by d 181
⌊x⌋ the floor of x 191
⌈x⌉ the ceiling of x 191
|x| the absolute value of x 187
gcd(a, b) the greatest common divisor of a and b 220
x := e x is assigned the value e 214
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&&&&&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
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Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Discrete_Mathematics_with_Applications_-_Susanna_Epp.pdf&&&
df&&&&&&&&&&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Subject Symbol Meaning Page
Sequences ... and so forth 227
n
ak the summation from k equals m to n of ak 230
k=m
n
ak the product from k equals m to n of ak 223
k=m
n! n factorial 237
Set a∈A a is an element of A 7
Theory a∈
/ A a is not an element of A 7
{a1 , a2 , . . . , an } the set with elements a1 , a2 , . . . , an 7
{x ∈ D | P(x)} the set of all x in D for which P(x) is true 8
R, R− , R+ , Rnonneg the sets of all real numbers, negative real 7, 8
numbers, positive real numbers, and
nonnegative real numbers
Z, Z− , Z+ , Znonneg the sets of all integers, negative integers, 7, 8
positive integers, and nonnegative integers
Q, Q− , Q+ , Qnonneg the sets of all rational numbers, negative 7, 8
rational numbers, positive rational numbers,
and nonnegative rational numbers
N the set of natural numbers 8
A⊆B A is a subset of B 9
A ⊆ B A is not a subset of B 9
A=B A equals B 339
A∪B A union B 341
A∩B A intersect B 341
B−A the difference of B minus A 341
Ac the complement of A 341
(x, y) ordered pair 11
(x 1 , x2 , . . . , xn ) ordered n-tuple 346
A×B the Cartesian product of A and B 12
A1 × A2 × · · · × An the Cartesian product of A1 , A2 , . . . , An 347
∅ the empty set 361
P( A) the power set of A 346
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
ons_-_Susanna_Epp.pdf&&&&&&&&&&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
usanna_Epp.pdf&&&&&&&&&&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Discrete_Mathematics_with_Applica
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,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Discrete_Mathematics_with_Applications_-_Susanna_Epp.pdf&&&&&&&&
Susanna_Epp.pdf&&&&&&&&&&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Discrete_Mathematics_with_App
_Epp.pdf&&&&&&&&&&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
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,~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Discrete_Mathematics_with_Applications_-_Susanna_Epp.pdf&&&
df&&&&&&&&&&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
List of Symbols
Subject Symbol Meaning Page
Logic ∼p not p 25
p∧q p and q 25
p∨q p or q 25
p ⊕ q or p XOR q p or q but not both p and q 28
P≡Q P is logically equivalent to Q 30
p→q if p then q 40
p↔q p if and only if q 45
∴ therefore 51
P(x) predicate in x 97
P(x) ⇒ Q(x) every element in the truth set for P(x) is in 104
the truth set for Q(x)
P(x) ⇔ Q(x) P(x) and Q(x) have identical truth sets 104
∀ for all 101
∃ there exists 103
Applications
of Logic NOT NOT-gate 67
AND AND-gate 67
OR OR-gate 67
NAND NAND-gate 75
NOR NOR-gate 75
| Sheffer stroke 74
↓ Peirce arrow 74
n2 number written in binary notation 78
n 10 number written in decimal notation 78
n 16 number written in hexadecimal notation 91
Number d |n d divides n 170
Theory and d /| n d does not divide n 172
Applications
n div d the integer quotient of n divided by d 181
n mod d the integer remainder of n divided by d 181
⌊x⌋ the floor of x 191
⌈x⌉ the ceiling of x 191
|x| the absolute value of x 187
gcd(a, b) the greatest common divisor of a and b 220
x := e x is assigned the value e 214
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Discrete_Mathematics_w
&&&&&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Discrete_Mathematics_with_Applications_-_Susanna_Epp.pdf&&&
df&&&&&&&&&&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Subject Symbol Meaning Page
Sequences ... and so forth 227
n
ak the summation from k equals m to n of ak 230
k=m
n
ak the product from k equals m to n of ak 223
k=m
n! n factorial 237
Set a∈A a is an element of A 7
Theory a∈
/ A a is not an element of A 7
{a1 , a2 , . . . , an } the set with elements a1 , a2 , . . . , an 7
{x ∈ D | P(x)} the set of all x in D for which P(x) is true 8
R, R− , R+ , Rnonneg the sets of all real numbers, negative real 7, 8
numbers, positive real numbers, and
nonnegative real numbers
Z, Z− , Z+ , Znonneg the sets of all integers, negative integers, 7, 8
positive integers, and nonnegative integers
Q, Q− , Q+ , Qnonneg the sets of all rational numbers, negative 7, 8
rational numbers, positive rational numbers,
and nonnegative rational numbers
N the set of natural numbers 8
A⊆B A is a subset of B 9
A ⊆ B A is not a subset of B 9
A=B A equals B 339
A∪B A union B 341
A∩B A intersect B 341
B−A the difference of B minus A 341
Ac the complement of A 341
(x, y) ordered pair 11
(x 1 , x2 , . . . , xn ) ordered n-tuple 346
A×B the Cartesian product of A and B 12
A1 × A2 × · · · × An the Cartesian product of A1 , A2 , . . . , An 347
∅ the empty set 361
P( A) the power set of A 346
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_OceanofPDF.com_Discrete_Mathematics_w
&&&&&&&&&&&&&@#%%%%%%%%%%%%%%%%%%%%%%%*!^(((((((((((((((((((((((((((((((((((((#&*^)(((((((((((((
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
