Download Math 211 Sets 2012

Math 211
Sets 2012
J
Candice
Casey
Amanda
Ashley W.
Kelly
Taylor
Tammy!
Ethan
Ronnie
A
C
Ronni
Jenny
Candice
Casey
Amanda
Ashley W.
Taylor
Tammy!
Ethan
Ronnie
Scott
Jenny
S
Tammy!
Amanda
G
Taylor
Candice
Tammy!
Casey
Kelly
Ashley W.
Ashley H.
Ethan
Ronni
T
E
Amanda
Ashley W.
Ethan
Candice
Casey
Jenny
Ashley H.
Taylor
Kelly
Scott
Tammy!
N
Tammy!
Ethan
Jenny
P
Candice
Taylor
Tammy!
Kelly
Ashley W.
Amanda
Ashley H.
Scott
M
Candice
Amanda
Ashley W.
Ethan
Ronni
Jenny
H
Candice
Casey
Amanda
Kelly
Ashley W.
Ronni
D
Candice
Casey
Ashley H.
Amanda
Ethan
Taylor
Kelly
Ashley W.
Scott
Jenny
R
Candice
Casey
Amanda
Taylor
Kelly
Ashley W.
Ashley H.
Scott
Ronni
Jenny
L
Ashley H.
Candice
Casey
Taylor
Kelly
Ashley W.
Amanda
Ethan
Scott
Ronni
Jenny
U
Amanda
Ashley H.
Ashley J.
Ashley W.
Candice
Casey
Ethan
Jenny
Kelly
Ronni
Scott
Tammy!
Taylor
Use your sets to learn the terminology and symbols we use for sets. This is called “set algebra.”
(1) True or false. If false, write another statement using the same symbol, but different sets, that is true.
(1) N ∈ E
____
(2) N ⊆ E
____
(3) P ⊂ U
____
____
(6) A ⊂ T
____
𝐴̅
____
(5) M ⊆ A
(7) H ~ P
____
(8) Amanda ∉ M
(4) U =
(9) Kelly ∈ G
____
____
Sets can be operated on! We have five operations to discuss.
The complement of a set:
̅
A
“not A”
A
The union of sets:
The intersection of sets:
A ∪B
A ∩ B “in A or B or both”
“in both A and B”
A
B
A – B “A minus B”
B
B
A x B The Cartesian Product—which is different!
̅ together:
Lets do S x D
A
A
B
With these we do set operations using Venn diagrams. So let’s get at it!
This table was online, and it is incomplete and has extra material, but I thought
you would like it anyway . . .
Table of set theory symbols
Symbol
{}
A∩B
A∪B
A⊆B
A⊂B
A⊄B
A⊇B
A⊃B
A⊅B
2A
Symbol Name
a collection of elements
A={3,7,9,14}, B={9,14,28}
objects that belong to set A
intersection
A ∩ B = {9,14}
and set B
objects that belong to set A
union
A ∪ B = {3,7,9,14,28}
or set B
subset has fewer elements or
subset
{9,14,28} ⊆ {9,14,28}
equal to the set
proper subset / strict subset has fewer elements
{9,14} ⊂ {9,14,28}
subset
than the set
left set not a subset of right
not subset
{9,66} ⊄ {9,14,28}
set
set A has more elements or
superset
{9,14,28} ⊇ {9,14,28}
equal to the set B
proper superset /
set A has more elements than
{9,14,28} ⊃ {9,14}
strict superset
set B
set A is not a superset of set
not superset
{9,14,28} ⊅ {9,66}
B
power set
all subsets of A
power set
A=B
equality
A\B
A-B
A∆B
Example
set
Ƥ (A)
Ac
Meaning / definition
all subsets of A
both sets have the same
members
all the objects that do not
complement
belong to set A
objects that belong to A and
relative complement
not to B
objects that belong to A and
relative complement
not to B
objects that belong to A or B
symmetric difference
but not to their intersection
A={3,9,14}, B={3,9,14}, A=B
A={3,9,14}, B={1,2,3}, AB={9,14}
A={3,9,14}, B={1,2,3}, AB={9,14}
A={3,9,14}, B={1,2,3}, A ∆
B={1,2,9,14}
symmetric difference
objects that belong to A or B A={3,9,14}, B={1,2,3}, A ⊖
but not to their intersection B={1,2,9,14}
a∈A
element of
set membership
A={3,9,14}, 3 ∈ A
x∉A
(a,b)
not element of
no set membership
A={3,9,14}, 1 ∉ A
ordered pair
collection of 2 elements
A⊖B
A×B
Cartesian product
|A|
cardinality
#A
cardinality
‫א‬
Ø
U
aleph
empty set
universal set
natural numbers /
whole numbers set
(with zero)
natural numbers /
whole numbers set
(without zero)
ℕ0
ℕ1
set of all ordered pairs from
A and B
the number of elements of set
A={3,9,14}, |A|=3
A
the number of elements of set
A={3,9,14}, #A=3
A
infinite cardinality
Ø={}
C = {Ø}
set of all possible values
ℕ0 = {0,1,2,3,4,...}
0 ∈ ℕ0
ℕ1 = {1,2,3,4,5,...}
6 ∈ ℕ1
ℤ = {...-3,-2,-1,0,1,2,3,...}
-6 ∈ ℤ
ℤ
integer numbers set
ℚ
rational numbers set ℚ = {x | x=a/b, a,b∈ℕ}
ℝ
real numbers set
ℂ
complex numbers set ℂ = {z | z=a+bi, ∞<a<∞,
-∞<b<∞}
ℝ = {x | -∞ < x <∞}
2/6 ∈ ℚ
6.343434 ∈ ℝ
6+2i ∈ ℂ
From http://www.rapidtables.com/math/symbols/Set_Symbols.htm accessed 10/01/12