MATHEMATICAL LOGIC

MATHEMATICAL LOGIC Techwithgyan.online discrete Math Descrete math Example
Mathematical Logic Theory 


MATHEMATICAL LOGIC


Propositional Logic: -

Propositional Logic is connected with statements assigned. The purpose is to analysis this statement either individually or in a composite manner.

Definition: -

A proposition is a collection of declarative statement that has either a true value “TRUE”or a true value “FALSE”. A proposition consist of propositional variables by capital latter. The connected the propositional variables.

EXAMPLE :-

“Man is mortal” it returns truth value “TRUE”

“12+3=3-2” it returns truth value “FALSE”

Connectives: -

  1. OR(V)

  2. AND (^)

  3. NEGATION/NOT (¬)

  4. implication/in – then ( )

  5. IF AND ONLY IF ()

OR(V): -

The OR operation of two propositions A and B (Written A V B) is true if at least any of the propositional value A or B is TRUE.

Truth Table :-

A

B

A^B

TRUE

TRUE

TRUE

TRUE

FALSE

TRUE

FALSE

TRUE 

TRUE

FALSE

FALSE

FALSE

AND (^):-

The AND operation of two proposition A and B (Written as A^B) is true if Both the propositional variable.

Truth Table :-

A

B

A^B

TRUE

TRUE

TRUE

TRUE 

FALSE

FALSE 

FALSE

TRUE

FALSE 

FALSE

FALSE

FALSE 

Negation/Not(¬):-

The Negation of proposition a (written as¬ A is FALSE when A is true and is true when is FALSE.

Truth Table :-

A

¬A

TRUE

FALSE

FALSE

TRUE

Implication/ If Then(→):-

AN IMPLICATION A→B is the proposition if “A “than “B” it is FALSE if A is TRUE and B is FALSE. The reset case is TRUE.



Truth Table:-

A

B

A→B

TURE 

TRUE

TRUE

TRUE

FALSE

FALSE

FALSE

TRUE

TRUE

FALSE

FALSE

TRUE

IF AND ONLY IF:(⇔)

A⇔B is Bi-conditional logical connective which is “TRUE” when A and B are same I.e Both are FALSE or both TRUE.

Truth table:-

B

A⇔B

TRUE

TRUE

TRUE

TRUE

FALSE

FALSE

FALSE

TRUE

FALSE

FALSE

FALSE

TRUE