Basic concepts of mathematical logic will be covered. This will help us to understand and construct mathematical reasoning and arguments.

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

# Addition
If we know that $q_1$ is true, we can consistently conclude that, $\left(q_1\lor q_2\right)$
is true. Here $q_2$ is an arbitrary proposition. This rule of inference is called addition. The following statement is always true.

"If $q_1$ is true then $q_1 \lor q_2$ is also true."

We can write this tautology as follows:

$$q_1 \Rightarrow \left(q_1\lor q_2\right).$$

## Examples
Let’s look at a few examples to see this rule in action.


Learn about more rules of inference for the construction and understanding of mathematical arguments.


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

Inference: Addition, Conjunction, and Simplification

Addition

Examples