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# Finite Math - Venn Diagrams and Partitions

## by Justin Tallant, Freelance Web Developer and entrepreneur at Home on Sep 13, 2011

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Finite Math

Finite Math
Venn Diagrams and Partitions

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## Finite Math - Venn Diagrams and PartitionsPresentation Transcript

• 1.2Venn Diagrams and Partitions
• Venn Diagram Graphic representation of sets: Big rectangle is Universal Set, Set A and B in circles
• Union and Intersectionon Venn Diagram Represented by shaded area: A U B: A ∩ B:
• Complements A’: B’:
• Complement with Unionand 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
• Quiz 1.2.1 Which of the following represent this Venn Diagram? A. A U B B. A’ ∩ B C. A ∩ B’
• Quiz 1.2.1 Which of the following represent this Venn Diagram? A. A U B B. A’ ∩ B C. A ∩ B’
• 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”
• 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
• 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.
• 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}
• 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
• Summary How to use and interpret Venn Diagram  Union/Intersection/Complement Deﬁnition:  Disjoint  Partition
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