1. Discrete Mathematics Lecture 6: Set and Function
By:
Nur Uddin, Ph.D

2. Motivation
Much of discrete mathematics is devoted to the study of discrete structures, used to represent discrete objects.
Many important discrete structures are built using sets, which are collections of objects.
Among the discrete structures built from sets are combinations, unordered collections of objects used extensively in counting; relations, sets of ordered pairs that represent relationships between objects; graphs, sets of vertices and edges that connect vertices; and finite state machines, used to model computing machines

3. Sets
Set is the fundamental discrete structure.
Definition:

4. Examples

5. Example

6. Mathematics set notation

7. Interval notation

8. Equal set
Example:

9. Empty set

10. Venn Diagrams Venn diagram is a graphically representation of sets.
Example:

11. Subsets

12. Subset Theorem

13. Proper subset

14. Subset of equal sets

15. Size of a Set
Examples:

16. Power Sets

17. Cartesian product

18. Cartesian products
Example:

19. Cartesian products

20. Cartesian products