Lecture Notes on Propositional Logic

Introduction to Propositional Logic

• Definition: Propositional logic studies ways of joining and modifying propositions to form more complex propositions.
• Focus Areas:
  • Combining propositions
  • Modifying propositions
  • Studying relationships and derived properties from combined propositions

Understanding Propositions

• Example Statement:
  • "Adam is good in playing football."
  • Combined: "Adam is good in playing football and he is representing his college at national level."
• Logical Connective: The word "AND" is used to combine two propositions (e.g., P and Q).

Modification of Propositions

• Example of Negation:
  • Statement: "I enjoy watching television."
  • Negation: "It is not the case that I enjoy watching television."
• Propositional Logic Functions:
  • Combine propositions
  • Modify propositions (e.g., negation)

Terminology

• Sentential Logic: Propositional logic is also known as sentential logic or statement logic, focusing on statements and their combinations.

Importance of Compound Propositions

• Definition: Compound propositions are created by combining one or more propositions.
• Reason for Use: Most mathematical statements are constructed by combining multiple propositions.

Propositional Variables

• Convenience: Using propositional variables simplifies the writing of complex statements.
  • Example Representations:
    • "Adam is good in playing football" represented as P
    • "He is representing his college at national level" represented as Q
    • Combined: P and Q (using AND operator)
• Definition: Propositional variables are variables that represent propositions.

Summary

• Propositional logic facilitates the reduction of complex statements into simpler forms using propositional variables and logical operators.
• Further discussions on operators will be covered in subsequent lectures.

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Conclusion

• Thank you for attending the lecture.