Sets and Set Theory Flashcards

1
Q

Sets

A

Unordered collections of objects that can be finite or infinite.

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2
Q

Elements

A

Members of the set

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3
Q

Singleton set

A

Set with exactly one element.

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4
Q

The ways to specify sets

A
  1. Description method
  2. Roster/Enumeration method
  3. Rule method (Set Builder Notation)
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5
Q

V = set of all vowels in the English alphabet

A

Description method.

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6
Q

V = {a, e, i, o, u}

A

Roster/Enumeration method.

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7
Q

A = {x|x is a perfect square less than 10}

A

Rule method.

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8
Q

Repeated elements are to be written _.

A

once

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9
Q

Cardinality

A

Number of elements in a set.

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10
Q

Symbol for cardinality

A

||

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11
Q

|S| could be _ or _, depending on the number of elements

A

finite, infinite

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12
Q

|{}|

A

0

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13
Q

|{{}}|

A

1

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14
Q

A

Set of natural numbers = {1, 2, 3, …}

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15
Q

W

A

Set of whole numbers = {0, 1, 2, …}

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16
Q

A

{ …, -2, -1, 0, 1, 2, … } = set of integers

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17
Q

ℤ+

A

{ 1, 2, 3, … } = set of positive integers

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18
Q

ℤ-

A

{ …, -3, -2, -1 } = set of negative integers

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19
Q

A

{ p/q | p,q E ℤ and q≠0 } = set of rational numbers

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20
Q

A

Set of real numbers

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21
Q

A

{ a + bi | a,b E ℝ, i = √(-1) } = set of complex numbers

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22
Q

A ⊆ B

A

Every element of A is an element of B

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23
Q

B ⊇ A

A

If and only if A ⊆ B

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24
Q

A = B

A

Every element of A is an element of B and every element of B is an element of A

25
A ⊂ B
Every element of A is an element of B and B has at least one element that is not in A
26
B ⊃ A
If and only if B ⊇ A and there exists an element that is in set B but not in A
27
Superset
28
Proper superset
29
Subset
30
Proper subset
31
Venn Diagrams
Used to visualise relationships of sets
32
Disjoint sets
Sets that have no common element
33
A U B
The elements are those in A or in B
34
A ∩ B
The elements are those in A and in B
35
A ∩ B are disjoint if...
A ∩ B = {}
36
A - B
Set Difference. The elements are those in A and not in B
37
A'
The elements are in U and not in A
38
Other ways to write A'
-A, or U-Ā
39
{}'
U
40
A U {}
A
41
{} ∩ U
{}
42
A - A
{}
43
Identities for Set Difference: If set A and B are equal then...
A–B = A–A = {}
44
Identities for Set Difference: When an empty set is subtracted from a set...
the result is that set itself (A – {} = A)
45
Identities for Set Difference: When a set is subtracted from an empty set...
the result is an empty set ( {} – A = {} }
46
Identities for Set Difference: When a superset is subtracted from a subset, the result is...
empty set (A – B = {}, if A ⊂ B)
47
Identities for Set Difference: If A and B are disjoint sets then...
A - B = A, and B - A = B
48
Logic and Sets Correspondence: v = _
U
49
Logic and Sets Correspondence: ^ = _
50
Logic and Sets Correspondence: ~ = _
51
Logic and Sets Correspondence: T = _
U
52
Logic and Sets Correspondence: F = _
{}
53
Logic and Sets Correspondence: Truth Table = __
Membership Table
54
Logic and Sets Correspondence: T = _ or _
E, 1
55
Logic and Sets Correspondence: F = _ or _
∉, 0
56
(x E A) is the same as...
~ (x E A), or x E A’
57
Irrational numbers
Any real number that cannot be expressed as the quotient of two integers.
58
Composite numbers
A positive integer that has at least one divisor other than 1 and itself. A positive integer that can be formed by multiplying two smaller positive integers.
59
Prime numbers
Numbers that have only 2 factors: 1 and themselves.