Finite Math Venn Diagrams and Partitions Visit http://finitehelp.com/ for more info

1. 1.2
Venn Diagrams and Partitions

2. Venn Diagram
 Graphic representation of sets:
 Big rectangle is Universal Set, Set A and B in
circles

3. Union and Intersection
on Venn Diagram
 Represented by shaded area:
 A U B:
 A ∩ B:

4. Complements
 A’:
 B’:

5. Complement with Union
and Intersections
 (A U B)’ [everything not in A U B]:
 A’ ∩ B’ [common area from A’ and B’]:
A’ B’ A’ ∩ B’
 Notice, they are the same thing

6. Quiz 1.2.1
 Which of the following represent this Venn Diagram?
A. A U B
B. A’ ∩ B
C. A ∩ B’

7. Quiz 1.2.1
 Which of the following represent this Venn Diagram?
A. A U B
B. A’ ∩ B
C. A ∩ B’

8. Quiz 1.2.1
 Which of the following represent this Venn Diagram?
A. A U B
B. A’ ∩ B
C. A ∩ B’
 Answer: C
Note: Another way to read C is “A without B”

9. Disjoint Sets
 Sets A and B are disjoint if there are no common
elements between them.
 Ex: A = {1, 3, 5}, B = {2, 4, 6}
A B

10. Partitions
 The partition of a set X are disjoint subsets
whose union is the set X.
 Ex: Let X = {days of the week}.
Let A = {Mon, Tues}, B = {Wed, Thu, Fri},
C = {Sat, Sun}
 A, B, and C are said to be a partition of X.

11. Quiz 1.2.2
 Let U = {outcome of one die roll}. Which of the
following sets are a partition of U?
A. X = {1, 2, 3}, Y = {4, 5, 6}
B. X = {1, 3, 5}, Y = {1, 2, 3}
C. X = {1, 2, 3, 4}, Y = {3, 4, 5, 6}

12. Quiz 1.2.2
 Let U = {outcome of one die roll}. Which of the
following sets are a partition of U?
A. X = {1, 2, 3}, Y = {4, 5, 6}
B. X = {1, 3, 5}, Y = {1, 2, 3}
C. X = {1, 2, 3, 4}, Y = {3, 4, 5, 6}
 Answer: A

13. Summary
 How to use and interpret Venn Diagram
 Union/Intersection/Complement
 Definition:
 Disjoint
 Partition

14.  Features
 27 Recorded Lectures
 Over 116 practice problems with recorded solutions
 Discussion boards/homework help
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