1 © 2008 Pearson Addison-Wesley. All rights reservedOrdered 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 SetsThe Cartesian product of sets A and B, written, is © 2008 Pearson Addison-Wesley. All rights reserved

3 Example: Finding Cartesian ProductsLet 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 ProductsCheckpoint: 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 ProductIf n(A) = a and n(B) = b, then © 2008 Pearson Addison-Wesley. All rights reserved

6 Example: Finding Cardinal Numbers of Cartesian ProductsIf 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 SetsDraw a Venn Diagram to represent the set © 2008 Pearson Addison-Wesley. All rights reserved

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

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

11 Example: Shading Venn Diagrams to Represent SetsCheckpoint: 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 reservedDe Morgan’s Laws For any sets A and B, © 2008 Pearson Addison-Wesley. All rights reserved