Contents

1. Mathematical Logic  

1. Introduction  

2. Connectives   

3. Implications  

4. Propositional Equivalences

5. Tautological Implications 

6. Normal Forms  

7. Theory of Inference for Statement Calculus  

8. Predicate Calculus  

2. Relations and Functions   

1. Introduction  

2. Functions     

3. Permutations and Combinations   

1. Introduction  

2. Principles of Counting    

3. Permutations  

4. Combinations  

4. Number of Non-negative Integer Solutions    

1. Introduction  

2. Integer solutions of linear equations 

3. Binomial Identities 

5. Principles of Inclusion and Exclusion

1. Introduction  

2. Principle of Inclusion and Exclusion  

3. Derangements  

6. Algebraic Structures

1. Introduction  

2. Algebraic System    

3. Groups Permutations 

4. Subgroups     

5. Group Code    

6. Decoding