****Survey of Math Study Guide and Review****
-Set Concepts
Counting Numbers (Natural Numbers) = {1,2,3,4,5……}
Null or Empty set contains no elements of a given set and is defined as empty brackets { }
Listing the elements of a set inside brackets, {}, is known as Roster form. Example: A= {1, 2, 3, 4}
is a roster form.
Another way to define a set is called Set-Builder Notation. For example let’s convert the roster
form above to Set-Builder Notation.
Set A consists of natural numbers less than 5 so therefore,
(
={|∈
) 5} or
<
= { |∈
}≤ 4
The number of elements in a set is known as the Cardinal Number, n(A). For example the roster
form above has 4 elements in its set, n(A) = 4
Sets are determined to be equal if and only if they contain the exact same elements.
Sets are determined to be equivalent if and only if they have the same cardinal number.
A set is finite if it contains no elements or the number of elements in the set is a natural
number. For example, set A above is Finite because it contains four(4) elements.
A set is infinite if it contains an unlimited amount of elements. For example the set of counting
numbers is infinite.
Set A is a subset, (
⊆ ), if and only if all the elements of A are also elements of B.
Set A is a proper subset, ( ⊂ ), if and only if all the elements of set A are elements of Set B
and Set B must contain at least one element that Set A does not include.
There are
possible subsets of a given finite set A, where n is the number of elements in that
set.
The complement of set A, symbolized by A’, is the set of all elements of a universal set that are
not listed in set A.
Example of Complement:
U = {1 2 3 4 5} and A = {3 4 5} then A’ = {1 2}
Intersection of sets A and B, symbolized by
are common to both A and B.
Union of set A and B, symbolized as
of set A or set B or both.
∩ , is the set containing all the elements that
∪ , is the set containing all elements that are members
BASIC LOG IC LAWS
De Morgan'. la w s
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