Chapter 1C - Sets and Venn Diagrams
Chapter 1C - Sets and Venn Diagrams
A Set is a collection of objects. Elements of the set are the individual objects, e.g., if x is an
element of a set S then we write x ∈ S . Sets are described by listing their members within
a pair of braces, { A
}. Set
Useisthree
dots,. . ., of
to objects.
indicate Elements
a continuing
pattern
if there
are too
a collection
of the
set are
the individual
objects, e
many members to list.
element of a set S then we write x ∈ S . Sets are described by listing their mem
braces,
{ of
}. Numbers
Use
three
dots,. . ., to indicate a continuing pattern if t
Chapter
1C a1C
- pair
Sets
and
Venn
Diagrams
Chapter
- ofSets
and
Venn
Diagrams
Sets
Chapter 1C - Sets and Venn Diagra
many members to list.
1.
Numbers
(counting
numbers)
etAisSet
a collection
of Natural
objects.
Elements
of
theofset
objects,
e.g.,
if
x isif an
Sets
of
Numbers
is a collection
of objects.
Elements
theare
setthe
areindividual
the individual
objects,
e.g.,
x is an
{1,
2,
3,
.
.
.}
(N)
A
Set
is
a
collection
of
objects.
Elements
of
set are the individual
ment
of
a
set
S
then
we
write
x
∈
S
.
Sets
are
described
by
listing
their
members
within
element of a set S then we write x ∈ S . Sets are described by listing their members the
within
element
a set
S then
we pattern
write
x if
∈ there
Sare
. Sets
air
of braces,
{ 2.
}.{Whole
Use
dots,.dots,.
. {0,
., to
indicate
a continuing
pattern
if there
too
Numbers
1,. .,
2,
3,
.} of
a pair
of braces,
}. three
Use
three
to. .indicate
a continuing
areare
toodescribed by listing
1.
Natural
Numbers
(counting
numbers)
a pair of braces, { }. Use three dots,. . ., to indicate a continuing p
ymany
members
to list.
members
to list.
{1,−1,
2,many
3,
3. Integers {. . . , −3, −2,
0,.1,. .}
2,members
3, .(N)
. .} to
(Z)list.
Numbers
SetsSets
of
x of Numbers
2.
Whole
Numbers
{0,
2, 3, . . .}
Sets of Numbers
: x, y ∈ Z y 6= 0 1,(Q)
4. Rational Numbers
y
3. Integers {. . . , −3, −2, −1, 0, 1, 2, 3, . . .} (Z)
. Natural
Numbers
(counting
numbers)
1. Natural
Numbers
(counting
numbers)
5.
Irrational
Numbers
are numbers that have non!
"
1. Natural Numbers
(counting numbers)
{1, 2,{1,
3, .2,
. .}
(N)
3, . . .} repeating
(N) and non-terminating
decimal expansion.
x
√ 4. Rational {1,
2, log
3, . .e.}≈ 2.7,
(N)
Numbers
: x, y ∈ Z y #= 0
(Q)
Examples are 2, base for natural
y
. Whole
Numbers
{0,
1,
2,
3,
.
.
.}
2. Whole Numbers
1, 2, 3, . . .}
π ≈ 3.14.{0, (I)
2. Whole Numbers {0, 1, 2, 3, . . .}
5.3, Irrational
Numbers are numbers that have non. Integers
{.
.
.
,
−3,
−2,
−1,
0,
1,
2,
.
.
.}
(Z)
3. Integers 6.{. Real
. . , −3,Numbers
−2, −1, 0, 1,
2, 3, . of
. .}all rational
(Z)
consist
and irrarepeating
and non-terminating
decimal
3.
Integers
−1, 0, 1,expansion.
2, 3, . . .} (Z)
!
"
√ {. . . , −3, −2,
!
"
tional numbers.
(R)
x x
Examples are 2, base for natural
log
e
≈ 2.7, "
!
. Rational
Numbers
: x, y: ∈x,Zy y∈#=Z 0y #= 0(Q) (Q)
4. Rational
Numbers
x
π ≈ 3.14.
(I)
y
Relationship
among
Sets
y
4. Rational
Numbers
: x, y ∈ Z y #= 0
(Q)
y
Given
sets Aare
andnumbers
B
. Irrational
Numbers
that that
have
non- non-consist of all rational and irra6. Real
Numbers
5. Irrational
Numbers
are numbers
have
5.expansion.
Irrational
Numbers
repeating
and
non-terminating
expansion.
numbers.
repeating
and non-terminating
decimal
Subset
A ⊂decimal
B tional
every
element
of A(R)
is an
element of are
B numbers that have non√
√
and non-terminating
decimal expansion.
Examples
areUnion
2, base
forAnatural
log e consisting
≈ repeating
√
Examples
are
2, base
forB natural
e2.7,
≈ 2.7,
∪
the setlog
of every element
of A and every element of B
Relationship
among
Examples
are
2,
base
for
natural
logSets
e ≈ 2.7,
π ≈ 3.14.
(I) (I)
π ≈ 3.14.
Interesection
A ∩ B the set of all
elements
in
both
A
and
B
π ≈ 3.14. (I)
empty
set
∅
set
containing
elements
. Real
Numbers
consist
of all
and
irraGiven
A
and
Bnoirra6. Real
Numbers
consist
ofrational
all sets
rational
and
6. Real Numbers consist of all rational and irrationaltional
numbers.
(R) and B we have
numbers.
Given sets A(R)
tional
(R)
Subset
A ⊂ numbers.
B every element
of A is an element of B
Relationship
among
Sets
Relationship
among
Sets
Union
A ∪ B the set consisting
of every element
of ASets
and every el
Relationship
among
Interesection
A ∩ B the set of all elements in both A and B
enGiven
sets A
and
sets
AB
and B
B containing no elements
empty setGiven sets
∅ A andset
bset
A⊂A
B ⊂ every
element
of A of
is an
of B of B
Subset
B every
element
A iselement
an element
Subset
B every
everyelement
elementofofBA is an element of B
ion
A∪B
the set
of every
element
ofAA⊂of
and
Union
A∪B
theconsisting
set consisting
of every
element
A and every
element of B
Union
A
∪
B
the
set
consisting
of every element of A an
eresection
the set
allofelements
in both
A and
InteresectionA ∩ B
A∩B
theofset
all elements
in both
AB
and B
Interesection
A ∩ B the set of all elements in both A and B
pty
set set ∅
no elements
empty
∅ set containing
set containing
no elements
empty set
∅
set containing no elements
If A and B have no elements in common we write A ∩ B = ∅ and we say that A and B are
disjoint.