Propositional logic - Discrete Mathematics Part 1- Theguiderworld

Proposition logic :

A Proposition is a declarative sentence or a statement which is either true or false. The purpose of the proposition logic is to analyse the statements either individually or in compound manner.

Examples for propositional logic :

" 6 + 7 = 13 ", will return value ' TRUE '.

" 7 + 7 = 13 ", will return value ' FALSE '.

Connectives :

Connectives can be known as the symbols or the signs used to connect two or more statements.

In propositional logic we use five connectives which are as :

AND ( ⋀ )

OR ( ⋁ )

NOT / Negation ( ㄱ )

Implies / if - then (→ )

if and only if (⇔ )

AND ( ⋀ ) :

The AND operation is used in two proposition A and B and is written as ( A ⋀ B ) and is read as ' A and B ' and it will return ' TRUE ' if the both given statements are true.

OR ( ⋁ ) :

The OR operation is used in two proposition A and B and is written as ( A ⋁ B ) and is read as ' A or B ' and it will return ' TRUE ' if one of the given statements is true.

NOT / Negation ( ㄱ ) :

The Negation of a proposition A will be written as ( ㄱA ) and will return ' TRUE ' if A is false and will return ' FALSE ' if A is true.

Implies / if - then (→ ) :

The implication operation in proposition is written as ( A → B ) and is read as ' if A then B '. It will return ' FALSE ' if A is true and B is false. The rest cases will be true.

if and only if (⇔ ) :

This is also known as biconditional logical connective which is written as ( A ⇔ B ). It will return TRUE if both the conditions or statements are same i.e either true or false.