Discrete Mathematics

Contents

1. Sets 

1.1 Set  

1.2 Subset     

1.3 Operations on sets 

2. Relations

2.1 Cartesian product

2.2 Relations  

2.3 Special types of relations   

2.4 Equivalence relation   

2.5 Partition of a set     

2.6 Composition of relations     

2.7 Transitive closure           

2.8 Solved examples 

3. Functions        

3.1 Function                     

3.2 Different ways of representing function  

3.3 Types of functions                       

3.4 Solved examples

4. Divisibility of Integers

4.1 Well ordering principle (WOP)            

4.2 Division algorithm                       

4.3 Divisors                                 

4.4 Prime integers                           

4.5 Composite integers                       

4.6 Common divisors                          

4.7 Greatest common divisor (G.C.D.)         

4.8 Euclidean algorithm                      

4.9 Relatively prime integers                

4.10 Least common multiple (LCM)              

4.11 Congruence modulo N                      

4.12 Properties of congruence modulo N        

4.13 Fermat’s theorem 

4.14 Solved examples  

5. Elementary Counting Principles     

5.1 Cardinality of a finite set        

5.2 Counting                           

5.3 Pigeonhole principle               

5.4 Solved examples 

6. Elementary Logic                   

6.1 Propositions (Statements)          

6.2 Logical connectives    

6.3 Tautology, contradiction and contingency 

6.4 Logical equivalence    

6.5 Logical quantifiers    

6.6 Solved examples

7. Methods of Proof 

7.1 Valid arguments  

7.2 Methods of a proof     

7.3 Principle of induction 

7.4 Solved examples  

8. Boolean Algebra and Circuits

8.1 Binary operations

8.2 Boolean algebra  

8.3 Boolean function 

8.4 Switching circuits     

8.5 Application of boolean algebra to switching circuits 

8.6 Solved Examples