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Set Operations - Union, Intersection, Complement




 
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A set is a well defined group of objects or symbols. The objects or symbols are called elements of the set. We will look at the following set operations: Union, Intersection and Complement.

Union of Sets
Learn about union of sets.
Example:
Set A = {1, 4, 6, 8}
Set B = {0, 2, 4, 8, 9},
U = {the digits}
Draw a Venn Diagram for A ∪ B
Intersection of Sets
Learn about intersection of sets.
Example:
Set A = {1, 4, 6, 8}
Set B = {0, 2, 4, 8, 9}
U = {the digits}
Draw a Venn Diagram for A ∩ B
Complement of a Set
Learn what a complement of a set is.
Example:
Set A = {0, 1, 4, 5, 6, 7, 8}
U = {the digits}
Draw a Venn Diagram for A'
Boolean Set Operations
Intersection, union and complement set operations defined
Example:
Universe = {1,2,3,4,5,6,7,8,9,10}
A = {2,4,6,8,10}
B = {6,7,8,9,10}



Sets - Intersection, Union and Complement
A ∩ B pronounced as A intersection B are members that are common to both set A and set B.
A ∪ B pronounced as A union B are members that are in set A or set B or both.
A' pronounced as A complement are members that are not in set A.
Example:
If U = {1,2,3,4,5,6,7,8,9,10}
A = {1,2,3,4,5,6}
B = {1,2,3,5,7}
C = {2,4} and D = {8,9}
Find
A ∩ B
A ∪ B
A'
A ∩ C
A ∪ C
B ∩ D
B ∪ D
B'
A ∩ B ∩ C
(A ∪ B)'
Set Operations and Venn Diagrams - Part 1 of 2
A Venn diagram is a visual diagram that shows the relationship of sets with one another.
The set of all elements being considered is called the universal set (U) and is represented by a rectangle.
The complement of A, A', is the set of elements in U but not in A. A' = {x|x ∈ U and x = ∉ A}
Set A and B are disjoint because they do not share any common elements.
B is a proper subset of A. This means B is a subset of A, but B ≠ A.
The intersection A and B is the set of elements in both set A and set B.
The union of A and B is the set of elements in set A or set B.
Intersection and Unions with the Empty Set
A ∩ ∅ = ∅
A ∪ ∅ = A
Set Operations and Venn Diagrams - Part 2 of 2
Examples:
1. Create a Venn diagram to show the relationship among the sets.
U is the set of whole numbers from 1 to 15.
A is the set of multiples of 3.
B is the set of primes.
C is the set of odd numbers

2. Given the following Venn diagram, determine each of the following sets.
1. A ∩ B.
2. A ∪ B
3. (A ∪ B)'
4. A' ∩ B
5. A ∪ B'


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