## Introduction

We know that the simple statements are represented as p, q and so on. Suppose we are given a compound preposition.

p ∧ q

There is another property of compound prepositions called the **duality. **The dual of the above statement is

p ∨ q

Therefore, the dual can be achieved by interchanging ∧ by ∨ or interchanging ∨ by ∧. This means ∧ and ∨ are dual of each other.

## Dual for another type of statement

We will see an example of another type of prepositional statement in which we use True or False directly instead of a variable.

For example,

p ∨ T

is a compound preposition which True as one of the variable.

The dual of such a statement can be obtained by interchanging ∨ by ∧ and interchanging True with False.

Each of the statement can be derived from the other.

## Understanding Duality using a Truth Table

These are the truth tables for statements

(p ∧ q)

and

(p ∨ q)

.

If we interchange the

(p ∧ q )

by

(p ∨ q)

.or

(p ∨ q)

. by

(p ∧ q )

, we get the dual of each other. The truth table validate this claim. We can check this for other prepositional statement also.