Section 2'3 Venn Diagrams and Set Operations

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Section 2.3 Venn Diagrams and Set Operations

• Thinking Mathematically
• Math 1001

2
Objectives

• Use Venn diagrams to visualize Set relationships.
• Perform operations with sets.

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Visualizing the Relationship Between Two Sets
(page 61)

• A - Would you be willing to donate blood?
• B - Would you be willing to help serve a free
  breakfast to blood donors?

Yes/No
No/Yes
No/No
Yes/Yes
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Disjoint Sets
Yes/No
No/Yes
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Proper Subsets
Willing to serve breakfast
Blood and breakfast
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Equal Sets
Breakfast
Blood
What if everyone who gave blood also was willing
to serve breakfast?
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Sets with some Common Elements
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Venn Diagrams
Disjoint sets have no elements in common.
The set B is a proper subset of A.
The sets A and B have some common elements.
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Definition of the Intersection of Two Sets (page
62)

• The intersection of sets A and B
• Is the set of elements common to both set A and
  set B.
• Set builder notation

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Example 1a Find the intersection of two sets.

• 7, 8, 9, 10, 11 n 6, 8, 10, 12
• 8, 10

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Intersection - Venn Diagrams
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Example 1b Find the intersection of two sets.

• 1, 3, 5, 7, 9 n 2, 4, 6, 8
• Ø

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Example 1c Find the intersection of two sets.

• 1, 3, 5, 7, 9 n Ø
• Ø

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Definition of the Union of Sets

• The union of sets A and B
• Is the set of elements that are members of set A
  or set B or of both sets.
• Set builder notation

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Example 2a Intersection - Venn Diagrams
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Example 2b Find the union of two sets.

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

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Example 2c Find the union of two sets.

• 1, 3, 5, 7, 9 U Ø
• 1, 3, 5, 7, 9

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The Empty set and U and n

• For and set A,

and
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Check Point 3a (page 65)

• Given U a, b, c, d, e, A b, c, and
• B b, c, e
• Find (A U B)
• Then find An B

a
d
a,d
B
A
b
e
c
a,d
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De Morgans Laws

• (A U B) An B
• (A n B) AU B

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Section 2.3 Homework

• Pg 65-66, 4-5, 8-9, 12, 16, 20, 24-25, 27, 29,
  31, 34-35, 38, 44, 48-49, 51, 54-55 57, 59, 62,
  65-66, 69, 72-73, 76-77, 80-82