Lecture: Propositional Calculus

Background Material

• Recursion
  
• Logical operations in C++ or Java
  

Reading

• Chapters 1 and 2 from OLI course on Logic and Proofs.

Topics

• Boolean Functions and Expressions
  • Motivation: Logical Reasoning
  • Boolean Functions
  • Syntax and Semantics of Boolean Expressions
  • Evaluating Boolean Expressions
  • Equivalence of Boolean Functions and Expressions
  • Truth Tables and Disjunctive Normal Form (DNF)
    
• Boolean Algebra and Simplification
  • Motivation: Simplifying Conditional Expressions
  • Rules of Boolean Algebra
  • Equational Reasoning and Simplification
  • Proofs using Truth Tables
  • Tautologies and Automatic Verification of Tautologies

Lecture Notes

• BoolExpr.pptx or BoolExpr.pdf
• BoolAlg.pptx or BoolAlg.pdf

Programs

• None.

Resources

• Chapter 12 of the Aho and Ullman text.

Assignments

• End of chapter quizzes in Chapters 1 and 2 and problem set following Chapter 2 of OLI text. This is required and must be done individually.
• questions.pptx or questions.pdf - these are the practice questions from class.