Propositional Logic

Definition

Roughly speaking, a proposition is a possible condition of the world about which we want to say something.
The area of logic deals with a proposition is called propositional logic.

Example

There are two propositions  in the example: I am stupid, I will not pass the test. In propositional logic the propositions can be represented by their text.

I am stupid.

I will not pass the test.

I am stupid and I will not pass the test.

Definition of Propositional Variables

Propositional variables use letters to represent it, just as letters used to represent numerical variables.

Examples

p, q, r, s, ........

Types of Truth Table

Negation Proposition

- takes only a single formula as its argument.

Conjunction Proposition

- an infix binary connective, takes two formulae as arguments. Uses of "and".

Disjunction Proposition

- also known as "inclusive or", and corresponds to some uses of "or".

Exclusive Or of Two Propositions

- is true if exactly one proposition is true.

Conditional Statement and Biconditional Statement

- conditional statement correspond to if-then construction.

- biconditional statement meaning of "if and only if".

Compound Proposition

- combination of logical connectives-negation, conjunction, disjunction, conditional statement, and biconditional statement to build up compound propositions involve any number of propositional variables.