Formal logic provides a systematic and rigorous framework for expressing and analyzing arguments, which enables learners to evaluate the validity of reasoning, fostering critical thinking skills. Proficiency in constructing and understanding proofs enhances problem-solving abilities, encourages precision in thought, and promotes clarity in communication.

In this course, you’ll explore propositions and logical connectives in propositional logic. Next, you’ll cover first-order logic, which extends the scope to include variables, quantifiers, and predicates. Next, the rules of inference are discussed which provide the logical steps required to establish the validity of mathematical statements. 

After taking this course, you’ll develop the skills to navigate and manipulate logical systems effectively. You’ll also acquire the essential toolkit for constructing rigorous and convincing mathematical proofs—a skill that is pivotal in advanced mathematics, computer science, and other analytical disciplines.

Introduction to Logic: Basics of Mathematical Reasoning

# What is negation?

**Negation** is a unary operator; it only requires one operand. Negation of a proposition is another proposition with the opposite truth value. We use the symbol $\neg p$ to denote the negation of a proposition $p$. Negation is also called the **NOT** operator. 


## Examples


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Consider the following propositions:
* $H$: Sara is taking a history course.
* $N$: Sara is *not* taking a history course. 

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$H$ is true only if Sara is taking a history course.
$N$ is true only when Sara is not taking a history course. 
Therefore,  $N \equiv \neg H$. 

Introduction

Propositional Logic

Basic Operations

Assessment-I

Propositional Toolkit

Assessment-II

Logical Reasoning

Assessment-III

Quantifiers and First Order Logic

Assessment-IV

Quantified Logical Reasoning

Assessment-V

Proving Theorems

Assessment-VI

Conclusion

Negation

What is negation?

Examples