# Chapter Sets and Venn Diagrams A Set is a

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```					                                   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
}. Use three dots,. . ., to indicate a continuing pattern if there are too
a pair of braces, { A Set is a collection of objects. Elements 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
- Sets braces, { }. Use Diagrams
Venn Diagrams
Chapter 1C a pair of andand of Numbers dots,. . ., to indicate a continuing pattern if t
Chapter 1C - Sets Sets Venn three
many members to list.   Chapter 1C - Sets and Venn Diagra
of objects. Elements (counting numbers)
et is a collection 1. Natural Numbers of the set are the individual objects, of Numbers is an
Sets e.g., e.g., if x
A Set is a collection of objects. Elements of the set are the individual objects, if x is an
{1, 2,write x ∈ S . Sets A Set is a collection of objects. Elements of the set are the individual
3, . . .} (N)
ment of a set a set S then we write x ∈ S . Setsdescribed by listing their their members within
element of S then we                             are are described by listing members within
}. }. Use dots,. ., 1, indicate a a a S then we write x ∈ . are
a of braces, { 2. Whole Numbers. {0,to 2, to indicate setcontinuing pattern if SareSets too
element
air pair of braces, { Use threethree dots,. . ., 3, . . .} of continuing pattern if theretheretoo are described by listing
y members to list. list.                1. Natural Numbers (counting numbers) . ., to indicate a continuing p
a pair of braces, { }. Use three dots,.
many members to
{1, 2, 0, . 2, . .} (Z)
3. Integers {. . . , −3, −2, −1,3, .1,.} 3, .(N) to list.
many members
of Numbers
SetsSets of Numbers
x
4. Rational NumbersWhole Numbers0{0, 1,(Q)3, . . .}
2.        : x, y ∈ Z y =         2,           Sets of Numbers
y
3. Integers {. . .          −2,
. Natural Numbers (counting numbers) numbers , −3,have −1, 0, 1, 2, 3, . . .} (Z)
Numbers (counting numbers)
1. Natural 5. Irrational Numbers are                            that     non-
1.
{1, 2,{1,.2,.} . . .} repeating and non-terminating Natural Numbers (counting numbers)
3, . 3, (N) (N)                                       decimal expansion.
√ 4. Rational {1, 2, 3, . .} x :
Examples are 2, base for natural log .e ≈ y(N)x, y ∈ Z y = 0
Numbers 2.7,                           (Q)
. Whole Numbers {0, 1,{0,3, .2,.} . . .}
2. Whole Numbers               2, 1, . 3,
π ≈ 3.14. (I)
2. Whole Numbers {0, 1, 2, 3, . . .}
,{. . . ,−2, −1, 0, 1, 2,5. .2,.} . of.} Numbers irra-
. Integers {. . . 6. Real Numbers0,3, Irrational rational and are numbers that have non-
3. Integers       −3, −3, −2, −1, 1, . 3, . (Z) (Z)
consist       all
3. and non-terminating decimal expansion.
repeating Integers {. . . , −3, −2, −1, 0, 1, 2, 3, . . .} (Z)
√
tional numbers. (R)
x x             Examples are 2, base for natural log e ≈ 2.7,
4. Rational Numbers : x, y: ∈ Zπy≈Z3.14. 0(Q) (Q)
. Rational Numbers                            x, y ∈= 0 = (I)
y
y     y              Relationship among Sets x : x, y ∈ Z y = 0
4. Rational Numbers                                  (Q)
y
5. Irrational Numbers B numbers have non-
Numbers and are 6. that Numbers consist of all rational and irra-
. Irrational Given sets Aare numbers Realthat have non-
5. Irrational
repeating and non-terminating decimal expansion. A(R) Numbers are numbers that have non-
A ⊂ B every numbers.
repeating √ non-terminating tional element of is an element of B
and
Subset √                         decimal expansion.
Examples 2, 2, forA ∪ B natural e consisting of and element of A and decimal expansion.
Examples are are base base naturalthe setlog repeatingevery non-terminating every element of B
Union                   for       log ≈ e2.7, 2.7,
≈            √
π ≈ 3.14. 3.14. (I)
π≈      (I)                                            Examples are Relationship among Sets≈ 2.7,
2, base for natural log e
Interesection        A ∩ B the set of all≈ 3.14. in both A and B
π  elements (I)
6. Numbers
. RealReal Numbers                     ∅ of all sets and irra-
empty consist of all rational A and Bno elements
set consistGiven set containing irra-
rational and
tional numbers. sets A and B we have
tional numbers.   (R) (R)                          6. Real Numbers consist of all rational and irra-
Given
Subset                 A ⊂ B every (R)
tional numbers. element of A is an element of B
Relationship among SetsSets
Relationship among
Union                  A ∪ B the set consisting of every element of A and every el
Relationship among Sets
en sets A and B B                          Interesection          A ∩ B the set of all elements in both A and B
Given sets A and
empty set                         B
Given sets A andset containing no elements
∅
bset
Subset        A ⊂ A ⊂ every element of A of anis an element of B
B B every element is A element of B
ion
Union         A ∪ B ∪ B set consisting of Subsetelement ofA ⊂ B every element ofof A is an element of B
every                A and every element B
A the the set consisting of every element of A and every element of B
A A the the set elements in both A andAand
Union                 ∪ B the set consisting of every element of A an
Interesection ∩ B ∩ B set of allof all elements in both A B B
eresection
pty set set ∅                                           Interesection      A ∩ B the set of all elements in both A and B
empty                 ∅ set containing no elements
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.

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