The document summarizes key topics to be covered in Lecture 01 on discrete mathematics including: propositions which are statements that are either true or false; truth tables; logical operators like conjunction, disjunction, exclusive OR, and implication; bi-conditional statements; compound propositions; precedence of logical operators; translating sentences; and Boolean searches and bit operations. Examples of propositions and non-propositions are provided.

1. LECTURE 01

2. Textbook
Discrete Mathematics & Its Applications
- Kenneth H. Rosen

3. Topics to be covered today
Proposition
Truth Table
Conjunction & Disjunction
Exclusive OR & Implication
Bi-conditional Statement
Compound Propositions
Logical Operator Precedence
Translating Sentences
Boolean Searches
Bit Operation

4. Proposition
A Proposition is a Statement that is
Either True or False
For Example:
1. Washington, D.C., is the capital of the United States of
America
2. Toronto is the capital of Canada
3. 1 + 1 = 2
4. 2 + 2 = 3

5. Proposition
Sentences that are NOT Propositions
1 & 2 are Not Propositions
Because they Don’t conclude anything
3 & 4 are Not Propositions
Because ‘x’ can be Anything

6. Truth Table
Here ‘ ¬ ’ is Negation Operator

7. Conjunction & Disjunction

8. Exclusive OR & Implication

9. Bi-conditional Statement

10. Compound Proposition

11. Precedence of Logical
Operators

12. Translating Sentences

13. Translating Sentences

14. Boolean Searches

15. Bit Operations