1. Discrete Structures MT217 Lecture 01

2. Course Objectives Express statements with the precision of formal logic Analyze arguments to test their validity Apply the basic properties and operations related to sets Apply to sets the basic properties and operations related to relations and functions

3. Course Objectives Define terms recursively Prove a formula using mathematical induction Prove statements using direct and indirect methods Compute probability of simple and conditional events

4. Course Objectives Identify and use the formulas of combinatorics in different problems Illustrate the basic definitions of graph theory and properties of graphs Relate each major topic in Discrete Mathematics to an application area in computing

5. Recommended Books Discrete Mathematics with Applications (second edition) by Susanna S. Epp Discrete Mathematics and Its Applications (sixth edition) by Kenneth H. Rosen Discrete Mathematics by Ross and Wright

6. MAIN TOPICS 1. Logic 2. Sets & Operations on sets 3. Relations & Their Properties 4. Functions 5. Sequences & Series 6. Recurrence Relations 7. Mathematical Induction 8. Loop Invariants 9. Loop Invariants 10. Combinatorics 11. Probability 12. Graphs and Trees

7. Marks Distribution Two Sessional Exam 25% Assignments and Quizzes 25% Final Exam 50%

8. Contact E-mail: zahidabbas@ciitvehari.edu.pk

9. What is Discrete Mathematics? Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic– do not vary smoothly in this way, but have distinct, separated values.

10. What is Discrete Mathematics? Discrete mathematics focuses on problems that are not over a continuous domain. For example, is it possible to visit 3 islands in a river with 6 bridges without crossing any bridge more than once? That is a discrete math problem (because there are a finite (fixed, discrete) number of bridges). Or, what is the smallest number of telephone lines needed to connect 200 cities? The numbers can be large and the logic can be complex, but these type of problems are different from finding an optimal value for a function where the domain can be 3, 3.14, 3.14159, or any real value.

11. What is Discrete Mathematics? Discrete Mathematics concerns processes that consist of a sequence of individual steps.

12. Logic Logic is the study of the principles and methods that distinguishes between a valid and an invalid argument.

13. Statement

14. Examples

15. TRUTH VALUES of Propositions

16. Examples

18. Not Propositions

19. Rule

20. Example

22. Understanding Statements

24. Compound Statement

25. Symbolic Representation

26. Logical Connectives

27. Examples

28. Translating from English to Symbols

33. Negation (~)

34. Truth Table

35. Truth Table for

36. Conjunction (^)

37. Truth Table for

38. Disjunction (ᴠ)

39. Truth Table for

40. Summary