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


# Sarmad's pet
Let's take a more complex scenario as follows:

**Scenario**

Sarmad has a pet, or he has a motorcycle. If he has a motorcycle, then he is tired. If Sarmad does not have a motorcycle, (then) he uses a taxi. If Sarmad is not tired, then he is in the kitchen. 

If Sarmad has a pet, then the pet is in the kitchen. If Sarmad and his pet are in the kitchen, (then) he offers tuna to his pet. If Sarmad offers tuna to his pet, (then) his pet is a cat. If Sarmad does not have a pet, then he is lonely.

Given that:

Sarmad is not lonely, or he is not using a taxi. 

And Sarmad is not tired.

Can we conclude from this information that, Sarmad's pet is a cat, and the pet is in the kitchen, and Sarmad offers tuna to his pet?


Bolster your concepts of mathematical proofs by working on a complicated scenario.


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

Mathematical Proofs: A Complex Scenario

Sarmad’s pet