Logical Equivalence | Propositional Logic | Discrete Mathematics

Embark on a journey through the intricacies of logical equivalence in propositional logic with this illuminating presentation. Tailored for both beginners and seasoned logicians, this PowerPoint serves as a definitive guide to understanding and applying logical equivalence in various contexts.

This presentation begins by laying a solid foundation, elucidating the fundamental principles of propositional logic. From there, we delve into the concept of logical equivalence, which lies at the heart of logical reasoning and deduction.

Key topics covered in this presentation include:

Introduction to Propositional Logic: Explore the basics of propositional logic, including propositions, logical connectives, truth tables, and logical formulas. Gain a clear understanding of how propositions and logical operators form the building blocks of logical reasoning.

Defining Logical Equivalence: Delve into the definition of logical equivalence and its significance in propositional logic. Understand how two logical statements are deemed equivalent when they have the same truth values under all possible interpretations.

Properties and Laws of Logical Equivalence: Uncover a plethora of laws and properties that govern logical equivalence, such as the commutative law, associative law, distributive law, De Morgan's laws, and idempotent laws. Learn how these properties can be leveraged to simplify logical expressions and proofs.

Proving Logical Equivalence: Master the art of proving logical equivalence using various techniques, including truth tables, logical equivalences, and logical manipulations. Explore strategies for transforming complex logical expressions into equivalent, more manageable forms.

Applications of Logical Equivalence: Discover real-world applications of logical equivalence in fields such as mathematics, computer science, philosophy, and artificial intelligence. Understand how logical equivalence serves as a powerful tool for simplifying logical circuits, optimizing algorithms, and verifying the correctness of logical systems.

Whether you're a student grappling with the intricacies of propositional logic or a researcher seeking deeper insights into logical reasoning, this PowerPoint presentation equips you with the knowledge and tools to navigate the realm of logical equivalence with confidence. Download now and embark on a transformative journey into the realm of propositional logic.

1. Name: Sampad Kar Student Code: BWU/BTA/22/225 Group: D Section: D2 Course: Discrete Mathematics Course Code: PCC-CSM405 SESSION: 2023-24

2. From Propositional Logic Logical EQUIVALENCE

3. INDEX Example 2 References What is Proposition What is Logical Connectives Logical Equivalence Example 1

4. What is Proposition??? An expression consisting of some letter, words and symbols is called a propositional if it is True or False. If the proposition is True, it is denoted by ‘T’ and if it is False , it is denoted by ‘F’. For example, a. The Sun Rises in the East [ T ] b. 2 > 5 [ F ]

5. What are Logical Connectives The particular words and symbols used to join two or more proposition into a single composite form is called logical connectives. For Example, Delhi is The Capital of India and 2+2 = 4 [ T ] The above proposition is a combination of two propositions joined by a connective ‘and’

6. Logical Equivalence Two statements are said to be logically equivalent (or equivalent) if they have the same truth value for every row of the truth table, that is if x y is a tautology. Symbolically, x y.

7. Example 1 Show That,

8. Example 2 Show That, p q (p q)^ (q p)

9. https://www.slideshare.net/fvsandoval/formal-logic-logical-equivalence https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/2%3A_Logic/2.5%3A_Logical_Equivalences https://en.wikipedia.org/wiki/Logical_equivalence REFERENCES

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