nitesh11-dk / clg-notes

Propositions and Connectives

• Truth Table
• PDNF
• Logical Implication
• Rules of Inference
• Validity and Satisfiability
• Compactness and Resolution
• Quantifiers
• Propositional Logic

Application of Truth Table and Laws of Propositions

• Logical Equivalence
• Normal Forms
  • DNF
  • CNF
  • PCNF
  • PDNF

Logical Implication and Rules of Inference

• Validity and Satisfiability
• Compactness and Resolution
• Quantifiers
• Application of Propositional Logic

Relation and Functions

1. Relation and Functions

1.1 Representation of Relation

• Explanation of relations
• Various methods to represent relations

1.2 Types of Relations

• Reflexive, Symmetric, and Transitive relations
• Equivalence relations and their properties

1.3 N-ary Relations

• Definition and examples of N-ary relations
• Applications of N-ary relations

1.4 Equivalence Class

• Definition of Equivalence Class
• Relation to equivalence relations

2. Partitions and Ordering Relations

2.1 Partitions

• Definition and examples of partitions in sets
• Applications and properties

2.2 Partial Ordering Relations

• Definition of partial ordering
• Concepts of chain and antichain

2.3 Hasse Diagram

• Definition and construction of Hasse diagrams
• Usage in representing partially ordered sets

2.4 Lattice

• Definition of a lattice
• Examples and applications

3. Functions

3.1 Functions and Types of Functions

• Definition of functions
• Types: Injective, Surjective, Bijective
• Properties and examples

3.2 Chain and Antichain in Functions

• Explanation of chain and antichain within functions