### Introduction

We learned about the statements which has a truth value. A statement can be** True or False, but not both.**You can make new statements from simple statements, such a statement is called a

**Compound Preposition or a Compound Statement.**

For example,

Let p and q be two statements,**p***: The triangle has three equal sides.***q***: The triangle is an equilateral triangle.*

The compound statement is a statement using these two statements,

**p ∧ q*** : The triangle has three equal sides and it is an equilateral triangle.***p ∨ q*** : The triangle has three equal sides and it is an equilateral triangle.*

We constructed the compound statements using simple statements by using a connective.

A connective is a logical symbol that connects two simple statements.

The are many connectives, they are listed below

**Name Symbol **

*and ∧ **or ∨ **implications –> **bi-conditionals <–>*

Note that there are rule associated with each of the logical connectives and we will discuss about them.

### Truth Table for Compound Statements

**p ∨ q**

**Rule** : If any of the variable p , q is True, then the statement is True, else it is false.

**p ∧ q**

*Rule : When both the variable p , q are True, then the statement is True, otherwise it is false.***p ⇒ q**

**Rule** : The only case when the statement is False is when p is True and q is False, where p implies q Otherwise, the statement is True.**p ⇔ q**

*Rule : When both the variables p , q are same then the statement is True, Otherwise , it is False.*