## Introductory Logic Fall 2020

PHIL 102 – Introductory Logic Fall 2020 Problem Set # 5 Due: Nov. 20 Late assignments will be penalized at a rate of 10% per day. Students are encouraged to collaborate with their peers, but each must write up and hand in their own assignments. Please make sure that your name, and the name of your teaching assistant, appear on the assignment. Group Study Sessions: We have organized a number of group study sessions in which a TA will be on hand to facilitate group work and to provide help with practice problems. They are designed to be a resource for everyone to work on problem sets. But you should particularly consider attending if you are finding the material difficult. Information about the times/locations of the sessions is posted on Blackboard (on the “Group Study” tab). Question 1 – Provide a proof that demonstrates the following claims. 4 points each A) ⊢ (P ∧ Q) → (Q ∨ R) B) ⊢ ¬ (P → Q) → ¬ (P ↔ Q) C) ⊢ [P → (Q → R)] → [(P → Q) → (P → R)] Question 2 – Provide a proof that demonstrates the following claims. 8 points each A) P and ¬ ¬ P are provably equivalent. B) F → (G ∧ H) and (F → G) ∧ (F → H) are provably equivalent. C) A → C and ¬ A ∨ C are provably equivalent. Question 3 – Provide a proof that demonstrates the following claims. 4 points each A) ¬ (P → Q) and Q are provably inconsistent. B) ¬ (A ∨ B), ¬B → A, ¬A are provably inconsistent. C) ¬ (M ∨ ¬ M) is provably inconsistent. Question 4 – Provide a proof that demonstrates the following claims. 4 points each A) P → Q, ¬ (Q ∧ ¬ R) → P ⊢ Q B) ¬ (A ∧ B) ⊢ ¬A ∨ ¬ B C) (B → G) → ¬ G ⊢ ¬ G Question 5 – 4 points each A) Suppose that Y ⊢ X. Does it follow that ⊢ Y → X ? Explain, with reference to particular rules of inference. (Note that “X”, “Y”, “Z”, and “W” are variables here, so could stand for any sentence in TFL, including complex ones). B) Suppose that X ⊢ Y and Y ⊢ Z. Does it follow that X ⊢ Z ? Explain your answer. (Note that “X” and “Y” are variables here, so could stand for any sentence in TFL, including complex ones).