Notes Unit One MAT114 Sets and Counting

MAT114 Unit One

Basic Set Concepts
Set Definition = A collection of objects whose contents can be
clearly determined.
The clear determination is called “well-defined”
 The collection of all good bands
o Not well defined (not a set)
 The collection of odd numbers
o Well defined (set)
 The collection of small numbers
o Not well defined (not a set)


Three Ways to Represent Sets


1. Word Description
P → set of U.S presidents who were elected between 1990 and
2010.
2. Roster Method (list everything)
P → {Bill Clinton, George W. Bush, Barack Obama}
3. Set Builder Notation
P → { X | X is a U.S President who was elected between 1990 and
2010}


Symbols Related to Sets:
Symbol Term

, ∅ or {} Empty set (Null set)
∊ In (element of)
∉ Not In (not element of)
n(A) Cardinal Number
Set Example:
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {0, 2, 4, 5, 6, 8}
B = {1, 3, 5, 7}
- Find n(B) = 4
- Is the statement 7∊A true or false? = False
- Is the statement 5∉B true or false? = False


Equal and Equivalent Sets


 Two sets are equal if they have the exact same elements.
“A=B”
 Two sets are equivalent if they have the same number of
elements.


A set C that is equal to set B
C = {1, 7, 5, 3}


A set D that is Equivalent but NOT equal to set B
D = {2, 0, 4, 8}


Comparing Sets
Subsets: The set A is a subset of the set B if every element of A is
also in B. “A⊆B”



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