Lecture Notes: Logic and Propositional Logic Practice

Introduction

• The session involves practicing logic exercises related to propositional logic.
• Exercises were sent via email titled "Chapter 5 Practice" and should be opened for this class.

Instructor's Offer

• One-on-one meetings are available for students with questions up until the final exam, except Saturdays.
• The class is being recorded for future reference.

Propositional Logic Review

Key Concepts

• S and T Statement
  • True when both propositions are true.
  • False if either or both propositions are false.
• Not both S and T: Represented as ~(S ∧ T). True if at least one is false.
• Not either S or T: Represented as ~(S ∨ T). True only when both are false.
• Logical Equivalences
  • Not both S and T = Not S or not T
  • Not either S or T = Not S and not T

Practice Exercises and Translation

Exercise Examples

1. Not (C): Cartier does not make cheap watches.
2. A ∧ ~N: Arizona has a national park, but Nebraska does not.
3. S ∨ T: Either Stanford or Tulane has an architecture school.
4. H ∧ B: Both Harvard and Baylor have medical schools.
5. C → L: If Chanel has a rosewood fragrance, then so does Lanvin.
6. L → C: If Lanvin has a rosewood fragrance, then Chanel does.
7. M ↔ P: Maren Dow writes inclusive editorials if and only if Paul Krugman does.
8. R → M: Reese wins Best Actress only if Martin wins Best Director.
9. G → A: Armani will launch a leather collection given that Gucci rejects skinny models.
10. C → P: The Colts winning implies Peyton Manning is a great quarterback.
11. B ∨ W: Bill Gates does not support malaria research unless Warren Buffett does.
12. M → (L ∧ B): Mercedes will introduce a hybrid model only if Lexus and BMW do.
13. M ∧ (E ∨ D): Mariah Carey sings pop and either Elton John sings rock or Diana Krall sings jazz.
14. (M ∧ E) ∨ D: Either Mariah Carey sings pop and Elton John sings rock, or Diana Krall sings jazz.
15. ~(J ∧ P): Not both Jaguar and Porsche make motorcycles.
16. ~J ∧ ~P: Both Jaguar and Porsche do not make motorcycles.
17. N ∨ S: Either Nokia or Seiko makes cell phones.
18. ~(F ∨ M): Not either Ferrari or Maserati makes economy cars.
19. ~F ∧ ~M: Neither Ferrari nor Maserati makes economy cars.
20. (~F ∨ ~M): Either Ferrari or Maserati does not make economy cars.

Exam Information

• The final exam (Exam 5) is similar in structure to previous exams with approximately 15 questions.
• The exam will have a time limit, possibly up to 2 hours.

Closing

• Students are encouraged to set up meetings for additional help.
• Recording of the session and answers to exercises will be provided.