# Mathematics | Introduction to Propositional Logic

Logic is the basis of all mathematical reasoning, and of all automated reasoning. The rules of logic specify the meaning of mathematical statements. These rules help us understand and reason with statements such as

such that

where

**Importance of Mathematical Logic**

The rules of logic give precise meaning to mathematical statements. Also logic has numerous applications in Computer Science, varying from design of digital circuits, to the construction of computer programs and verification of correctness of programs.

**Propositional Logic**

**What is a proposition?**

A proposition is the basic building block of logic. It is defined as a declarative sentence that is either True or False, but not both.

The **Truth Value** of a proposition is True(denoted as T) if it is a true statement, and False(denoted as F) if it is a false statement.

For Example,

1. The sun rises in the East and sets in the West.

2. 1 + 1 = 2

3. 'b' is a vowel.

All of the above sentences are propositions, where the first two are Valid(True) and the third one is Invalid (False).

Some sentences that do not have a truth value or may have more than one truth value are not propositions.

For Example,

1. What time is it?

2. Go out and play.

To represent propositions, **propositional variables** are used. By Convention, these variables are represented by small alphabets such as

.

The area of logic which deals with propositions is called **propositional calculus** or **propositional logic**.

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