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Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 2.3, Slide 1
Set Theory2
Using Mathematics to Classify Objects
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 2.3, Slide 2
Set Operations2.3• Perform the set operations of union,
intersection, complement, and difference
• Understand the order in which to perform set operations
• Know how to apply DeMorgan’s laws in set theory
(continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 2.3, Slide 3
Set Operations2.3
• Use Venn diagrams to prove or disprove set theory statements
• Calculate the cardinal number of the union of two sets
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.3, Slide 4
Union of Sets
• Example: Find the union of the two sets.
1, 3, 5, 6, 8
2, 3, 6, 7, 8
1, 2, 3, 5, 6, 7, 8
A
B
A B
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.3, Slide 5
Intersection of Sets
• Example: Find the intersection of the two sets.
1, 3, 5, 6, 8
2, 3, 6, 7, 8
3, 6, 8
A
B
A B
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.3, Slide 6
Set Complement
• Example: Given U, find the complement of A.
1, 2, 3, , 10
1, 3, 5, 7, 9
2, 4, 6, 8, 10
U
A
A
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.3, Slide 7
Set Difference
• Example: Find the difference.
3, 6, 9, 12 : is an odd integer x x
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.3, Slide 8
Order of Set Operations
• Example: Let 1,2,3, ,10 , : is even ,U E x x
1,3,4,5,8 , and 1,2,4,7,8 .
Find .
B A
A B E A
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.3, Slide 9
Order of Set Operations
• Intersection distributes over union.
A B C A B A C
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.3, Slide 10
Order of Set Operations
