This lecture covers propositional equivalences like tautology and contradiction, logical equivalences that have the same truth values, De Morgan's law, and predicates and quantifiers. Predicates assign properties to variables, and quantifiers like the universal and existential quantifier specify whether a property holds for all or some variables. The lecture also discusses binding variables and nested quantified expressions.

1. LECTURE 02

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

3. Topics to be covered today
Propositional Equivalences
Predicates
Quantifier

4. Propositional Equivalences
Tautology
A compound proposition that is always true
No matter what the truth values of the propositions are
Contradiction
A compound proposition that is always false
Contingency
A compound proposition that is neither a tautology nor a contradiction

5. Logical Equivalences
Compound propositions that have the same truth values in all possible
cases
Are called Logically Equivalent

6. Logical Equivalences

7. Logical Equivalences

8. Logical Equivalences

9. De Morgan’s Law

10. Logical Equivalences

11. Logical Equivalences

12. Predicates

13. Predicates

14. Quantifiers
Universal Quantifier

15. Universal Quantifier

16. Universal Quantifier

17. Existential Quantifier

18. Existential Quantifier

19. Existential Quantifier

20. Binding Variables

21. Negative Quantified Expression

22. Nested Quantifiers

23. Nested Quantifiers