1. © 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

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

3. 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

4. Example: Finding Cartesian Products
Checkpoint: Let UA = {a, e, i, o, u}, A = {a, e}, UB = ℕ, and B = {1, 2, 3}
Find B x A’
© 2008 Pearson Addison-Wesley. All rights reserved

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

6. 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

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

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

9. Example: Shading Venn Diagrams to Represent Sets
Checkpoint: Draw a Venn Diagram to represent the set 𝐴′∪𝐵′.
© 2008 Pearson Addison-Wesley. All rights reserved

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

11. Example: Shading Venn Diagrams to Represent Sets
Checkpoint: Draw a Venn Diagram to represent the set 𝐴∪( 𝐵 ′ ∩𝐶).
© 2008 Pearson Addison-Wesley. All rights reserved

12. © 2008 Pearson Addison-Wesley. All rights reserved
De Morgan’s Laws
For any sets A and B,
© 2008 Pearson Addison-Wesley. All rights reserved