Section 2'2 Venn Diagrams and Subsets

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Section 2.2 Venn Diagrams and Subsets

• Thinking Mathematically
• Math 1001

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Objectives

• Understand the meaning of a universal set.
• Understand the basic ideas of Venn Diagrams.
• Find the complement of a set.
• Use the symbols
• Determine the number of subsets of a set.

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Definition of a Universal Set (page 50)

• A universal set, symbolized by U, is a set that
  contains all the elements being considered in a
  given discussion or problem.
• A Cats, A Chorus Line, Evita
• B The Producers, Grease
• What is the universal set?
• Broadway Musicals

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John Venn

• Born 4 Aug 1834 in Hull, England
• Died 4 April 1923 in Cambridge, England
• http//www-history.mcs.st-andrews.ac.uk/Mathematic
  ians/Venn.html

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Venn Diagram
U
A
B
Use this link to explore Venn diagrams.
http//nlvm.usu.edu/en/nav/vlibrary.html
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Example 2 Finding a Complement

• U 1, 2, 3, 4, 5, 6, 7, 8, 9
• A 1, 3, 4, 7
• Find A
• A 2, 5, 6, 8, 9

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Example 3 Using a Venn Diagram

• U 1, 2, 3, 4, 5, 6, 7, 8, 9
• A 1, 3, 4, 7
• Find A
• A 2, 5, 6, 8, 9

U
8
1
3
2
4
5
7
A
6
9
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Definition of a Subset of a Set (page 52).

• Set A is a subset of set B, expressed as
• if every element in set A is also an element in
  set B.

This notation means that A is not a subset of B.
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Consider these sets.

• A 1, 2, 3 B 3, 2, 1 C 1, 2, 3, 4
• Is A a subset of B?
• Is A a subset of C?
• Is B a subset of A?
• Is B a subset of C?

Yes
Yes
Yes
Yes
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Definition of a Proper Subset of a Set (page 54)

• Set A is a proper subset of set B, expressed as
• if set A is a subset of set B and sets A and B
  are not equal. A ? B

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Consider these sets.

• A 1, 2, 3 B 3, 2, 1 C 1, 2, 3, 4
• Is A a proper subset of B?
• Is A a proper subset of C?
• Is B a proper subset of A?
• Is B a proper subset of C?

NO
Yes
NO
Yes
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The Empty Set as a Subset

• For any set B,
• For any set B other than the empty set,

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The number of subsets of a given set.

• Make a table and list all of the subsets of W, X,
  Y, and Z
• W
• X a
• Y a, b
• Z a, b, c

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Homework 2.2

• Pg 58-60, 1, 3, 5, 6, 13-16, 19-21, 27-31, 34,
  36-40, 43-49,