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23 Cards in this Set

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Set
a collection of objects, which are called elements.
3 Methods Used to Indicate Sets
1) Description
2) Roster Form
3) Set-Builder Notation
Description of Sets
-use words
-a simple sentence

Ex: The set of blue items.
The set of triangles
Roster Form
-listing all elements in the set
-use braces { }

Ex: {yellow triangle, blue triangle}
Set-Builder Notation
-uses symbols

Ex: D= {x I x is a triangle}
Natural Numbers
{1, 2, 3, 4, ...}

symbol: N
Whole Numbers
{0, 1, 2, ,3, ...}
Integers
{..., -2, -1, 0, 1, 2, ...}
Finite
-has a stopping point
-"countable"
Infinite
-never ending
-fractions
Equality of Sets
Sets A and B are equal if they contain exactly the same elements.

Ex: A= {1, 2, 3} B= {3, 1, 2} A=B
Equivalent of Sets
-Contain the same number of elements

Ex: A= {a, b, c} B= {d, e, f}
Cardinality
-How many elements are in the set
-written as: n(A)

Ex: A= {a, c, 1, 4, 5) n(A)=5
Null or Empty Set
-no elements in the set
-written as { } or ∅
Universal Set
-All elements in the context of the problem
-written as U
Subset
A is a subset of B if and only if all elements of A are contained in B
Proper Subset
A is a proper subset of B if and only if A is a subset of B AND A does not equal B.
{}
is a subset of every set and a proper subset
Number of Subsets
2 , where n is the number of elements in the set
Complement
A all elements not in A
Union
A B
or
Intersection
A B
and
Number of Proper subsets
2 -1