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Set Theory
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Terms in this set (34)
Sets
Collection of objects whose contents can be clearly determined
Descriptive Form
Describing the members of the set using words
Roster Form
Listing elements of a set inside the braces, {}
Set-Builder Notation
describe a set by saying what properties its members have
W= {x|x is a day of the week}
Set W is the set of all elements such that are a day of the week
Empty Set
Also called the Null Set, the set that contains NO elments
Empty Set - Symbol
∅ OR {} but NEVER those combined
Element of a set - Symbol
∈
NOT an Element of a set - Symbol
∉
Natural Numbers
Positive whole numbers greater than zero
Cardinality
The number of distinct elements in a set
Cardinality Number - Symbol
n(A) and read as "n of A"
Equivalent Sets
Set A & set B contain the same number of elements; n(A)=n(B)
Equal Sets
Set A & set B contain exactly the same elements regardless of the order or possible repetition of elements; A=B
Finite Sets
For a set A, the n(A)=0 or n(A)=a natural number
Infinite Sets
For a set A, the n(A)=not a natural number or zero
Subset
If every element in set A is also in set B; Represented as A⊆B
Set A is not a subset of Set B - Symbol
A⊄B
Subsets & Empty Sets
The empty set is a subset of every set
Calculate the number of subsets within a set.
2 to the power of the set's cardinality
Universal Set
The general set that contains all elements under discussion.
Disjoint Sets
Two sets that have NO elements in common
Complement of a Set
The set of all elements in the universal set, but that are NOT in set A; A'
Intersection of Sets
It is the set of elements common to both set A and set B, A∩B
Union of Sets
It is the set of elements that are members of set A or set B or both sets; A∪B
Empty Set: Intersection
A∩∅ = ∅
Empty Set: Union
A∪∅= A
Proper Subset
If every element in set A is also in set B (not equal to set B); Represented as A⊂B
Set of x and y
{x, y}
Ordered pair of x and y
(x, y)
Integers
{ ... , -3, -2, -1, 0, 1, 2, 3, ... }
Rational Numbers
Numbers that can be written as the ratio of two integers, excluding the denominator equaling 0
Cartesian Product
Set of all possible ordered pairs, in which each of the elements of the first set are paired to each of the elements in the second set.
Difference of Sets
It is the set of elements that remain from a set after the common elements in the other set are removed.
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