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Chapter 2 The Basic Concepts of Set Theory

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1 Chapter 2 The Basic Concepts of Set Theory
© 2008 Pearson Addison-Wesley. All rights reserved

2 Section 2-3 Chapter 1 Set Operations and Cartesian Products
© 2008 Pearson Addison-Wesley. All rights reserved

3 Set Operations and Cartesian Products
Intersection of Sets Union of Sets Difference of Sets Ordered Pairs Cartesian Product of Sets Venn Diagrams De Morgan’s Laws © 2008 Pearson Addison-Wesley. All rights reserved

4 © 2008 Pearson Addison-Wesley. All rights reserved
Intersection of Sets The intersection of sets A and B, written is the set of elements common to both A and B, or © 2008 Pearson Addison-Wesley. All rights reserved

5 Example: Intersection of Sets
Find each intersection. a) b) Solution © 2008 Pearson Addison-Wesley. All rights reserved

6 © 2008 Pearson Addison-Wesley. All rights reserved
Union of Sets The union of sets A and B, written is the set of elements belonging to either of the sets, or © 2008 Pearson Addison-Wesley. All rights reserved

7 © 2008 Pearson Addison-Wesley. All rights reserved
Example: Union of Sets Find each union. a) b) Solution © 2008 Pearson Addison-Wesley. All rights reserved

8 © 2008 Pearson Addison-Wesley. All rights reserved
Difference of Sets The difference of sets A and B, written A – B, is the set of elements belonging to set A and not to set B, or © 2008 Pearson Addison-Wesley. All rights reserved

9 Example: Difference of Sets
Let U = {a, b, c, d, e, f, g, h}, A = {a, b, c, e, h}, B = {c, e, g}, and C = {a, c, d, g, e}. Find each set. a) b) Solution a) {a, b, h} © 2008 Pearson Addison-Wesley. All rights reserved

10 © 2008 Pearson Addison-Wesley. All rights reserved
Ordered Pairs In the ordered pair (a, b), a is called the first component and b is called the second component. In general Two ordered pairs are equal provided that their first components are equal and their second components are equal. © 2008 Pearson Addison-Wesley. All rights reserved

11 Cartesian Product of Sets
The Cartesian product of sets A and B, written, is © 2008 Pearson Addison-Wesley. All rights reserved

12 Example: Finding Cartesian Products
Let A = {a, b}, B = {1, 2, 3} Find each set. a) b) Solution a) {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)} b) {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)} © 2008 Pearson Addison-Wesley. All rights reserved

13 Cardinal Number of a Cartesian Product
If n(A) = a and n(B) = b, then © 2008 Pearson Addison-Wesley. All rights reserved

14 Example: Finding Cardinal Numbers of Cartesian Products
If n(A) = 12 and n(B) = 7, then find Solution © 2008 Pearson Addison-Wesley. All rights reserved

15 Venn Diagrams of Set Operations
B A B U U A A B U U © 2008 Pearson Addison-Wesley. All rights reserved

16 Example: Shading Venn Diagrams to Represent Sets
Draw a Venn Diagram to represent the set Solution A B U © 2008 Pearson Addison-Wesley. All rights reserved

17 Example: Shading Venn Diagrams to Represent Sets
Draw a Venn Diagram to represent the set Solution B A C U © 2008 Pearson Addison-Wesley. All rights reserved

18 © 2008 Pearson Addison-Wesley. All rights reserved
De Morgan’s Laws For any sets A and B, © 2008 Pearson Addison-Wesley. All rights reserved

19 © 2008 Pearson Addison-Wesley. All rights reserved
Using the Laws If U={a, b, c, d, e, f, g, h}, A={a, c, e, g} and B={b, c, d, e}, find © 2008 Pearson Addison-Wesley. All rights reserved


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