Propositional logic - Discrete Mathematics Part 2

Conditional statements :

    The If - then form ( p → q ) that we have learned previously is also known as the conditional statement. Mainly it has two parts :

• p - Hypothesis

• q - Conclusion

Converse, Inverse and Contrapositive :

Converse :

    The converse of any conditional statement is calculated by changing the order of the statements or in other words interchanging of Hypothesis and Conclusion.

For example :  The converse of p → q will be q → p.

Inverse :

    The inverse of any conditional statement is calculated by putting negation to both the statements or in other words negation of Hypothesis and Conclusion.

For example :  The inverse of p → q will be ㄱp → ㄱq.

Contrapositive :

    The contrapositive of any conditional statement is calculated by changing the order and putting negation to the statements or in other words interchanging and doing negation of Hypothesis and Conclusion.

For example :  The contrapositive of p → q will be ㄱq → ㄱp.    

Eample showing converse, inverse and contrapositive of a statement :

" If I am rich, then I will be happy. "

Converse : " If I will be happy, then I am rich. "

Inverse : " If I am not rich, then I will be not happy. "

Contrapositive : " If I will be not happy, then I am not rich. "

Normal Forms 

We can convert the proposition in two normal forms :

• Conjuctive Normal Form ( CNF )

• Disjuctive Normal Form ( DNF )

Conjuctive Normal Form : 

    A compound statement is said as conjuctive normal form if it is obtained by using AND operation among the variables and connecting them through OR. 
For example : 
    ( A ⋀ B ) ⋁ ( B ⋀ C ) ⋁ ( A ⋀ B ⋀ C )

Disjuctive Normal Form : 

    A compound statement is said as disjuctive normal form if it is obtained by using OR operation among the variables and connecting them through AND. 
For example : 
    ( A ⋁ B ) ⋀ ( B ⋁ C ) ⋀ ( A ⋁ B ⋁ C )

    Propositional logic part 1