Contents

1. Logic
1. Introduction
2. Propositional Logic
    Proposition
    Propositional Variable
    Logical Connectives
    Examples
3. Propositional Equivalences
    Definitions
    Logical Equivalences
    Examples
    Logical Equivalences involving Conditional and Biconditionals
    Constructing New Logical Equivalences
    Examples
4. Rules of Inference
4.1 Argument in Propositional Logic
      Valid Argument
      Fallacy
4.2 Rules of Inference for Propositional Logic
      Validity of Arguments
4.3  Using Rules of Inference to Build Arguments
      Examples
5. Predicates and Quantifiers
5.1 Predicates
      n-Place Predicate (or n-ary Predicate)
      Examples
5.2  Quantification and Quantifiers
     Universal Quantifier
     Existential Quantifier
     Examples
     Other Quantifiers
      Logical Equivalences Involving Quantifiers
      Negating Quantified Expressions
      Examples
2. Lattices and Boolean Algebra
1.  Introduction
     Definition
1.1  Types of Relations
      Reflexive Relation
      Symmetric Relation
      Transitive Relation
     Anti-Symmetric Relation
     Inverse Relation
     Equivalence Relation
     Partial Order Relation
     Examples
2. Digraphs of Relations
2.1 Matrix Representation and Composition of Relations
2.2 Composition of Relations
Examples
2.3 Transitive Closure and Warshall's Algorithm
2.4 Warshall’s Algorithm
Examples
3. Poset (Partially Ordered Set)
3.1 Partially Ordered Set (or Poset)
Definition
Examples4
3.2 Comparibility
3.3 Totally Ordered Set
3.4 Hasse Diagram7
Examples
Maximal and Minimal Elements
Definitions

4. Lattices
Definition
Examples
Definitions

Complement of Element
Examples
5. Boolean Functions
5.1 Operations in Boolean Algebra
Examples
5.2  Boolean Expressions and Boolean Functions
Definitions
5.3 Boolean Expression

Examples
Some definitions
5.4 Identities of Boolean Algebra
Examples
6. Duality
Dual Function
Duality Principle
Examples
6.1 Definition of Boolean Algebra
Examples
7.  Representing Boolean Function
Examples
Definitions
7.1 Disjunctive Normal Form (DNF): [or Sum of Products Expansion]
Definition
Examples
Definition
7.2 Conjunctive Normal Form (CNF): [or Product-of-Sums Expansion]
Definition
Examples

3. Counting Principles
1. Introduction
2. Cardinality of Set
Definitions
Examples
3. Cartesian Product of Sets
4. Basics of Counting
4.1 The Product Rule [or Multiplication Principle]
Examples
4.2 The Sum Rule [or Addition Principle]
Examples
4.3 The Principle of Inclusion Exclusion
Examples
5. The Pigeonhole Principle
Examples
5.1 The Generalized Pigeonhole Principle
Examples
5.2 Applications of Pigeonhole Principle
Examples
6. Generalized Permutations and Combinations
6.1 Permutation with Repetition
6.2 Combinations with Repetition
6.3 Permutations with Indistinguishable Objects
Examples
6.4    Distributing Objects into Boxes    39

4. Recurrence Relations
1. Introduction
2. Recurrence Relation
Examples
3. Linear Recurrence Relations with Constant Coefficients
Definition
Examples
4. Homogeneous Solutions
Definition
Method to Obtain Homogeneous Solutions
Examples
5. Particular Solutions
Examples
6. Total Solutions
Examples    31