What is Propositional logic? - Discrete Mathematics|Ugc net Computer Science

 Hi  Everyone,

Welcome to My blog,

Propositional Logic,

In this post,let us understand the basics of the Propositional logic of discrete mathematics in a simple way.

What does Propositional means?

• Propositional means statement-based
• It deals only declarative statement which means it is true or false ,but not both

What is Logic?

            Logic means rules and methods of correct reasoning.

• It decides whether the statement true or false.
• It combine statements and reasoning correctly.
• It avoid wrong conclusions.

What is Propositional Logic?

Propositional Logic is the branch of logic that deals with declarative statement (true/false) and their combinations using logic connectives.

Definition:

Propositional logic studies how propositions are connected and how their truth values are determined.

For example:

1. 2+2=4 .
2. 5+7=14.
3. 20<10.

Explanation:

In the above example, 1 is true,2 and 3 is false.

This is Propositional logic.next we see what statement is not Propositional logic.

For example:

1. Close the door
2. Find x value:x+2=4
3. x>3

In the above example,first statement looks like command .Second statement is question form.Third statement is also question form and the x value is not known. These statements are not Propositional logic .

Basic logic operations

Conjunction ( p ∧ q )

Truth Table 

    p        q             p ∧ q 

    

    T          T              T

    T          F              F

    F          T              F

    F          F              F

Explanation:

In the above Truth Table, Conjunction means like AND operator.If p and q is true ,the result is true.Otherwise the result is false.

Disjunction (p ∨ q)

Truth Table

p.         q.        p ∨ q

T          T        T

T          F        T

F          T        T

F          F        F

Explanation: 

 

In the above Truth Table, Disjunction means OR operator.If p or q is true,the result is true . Otherwise the result is false.

Negation ¬p

Truth Table

p         ¬p

T           F

F           T

Explanation:

In the above truth Table, Negation means it is opposite of given proposition.if p is true, negation of p is false.negation has only one proposition.

Implication(If-then)

p         q         p → q.

T          T          T

T          F          F

F          T          T

F          F          T

Explanation:

        In the above truth Table, implication means conditional statement. That means  the result is false, when p is true and q is false.otherwise,the result is true.implication is also known as conditional statements.

Biconditional (if and only if)

p.        q.       p ↔ q

T          T          T

T          F          F

F          T          F

F          F          T

Explanation:

In the above truth Table, Biconditional means the p and q are same ,the result is true . otherwise the result is false.

Conclusion:

I hope,this post will help you and give the clear explanation of the Propositional logic in the  discrete mathematics.If you like this post,like and share my blog with your friends,and follow my blog.