Assignment 4 Due Oct. 10, 2023 Answer all of the following questions. Questions values are indicated at the beginning of each question. The maximum grade for the assignment is 20 points. The assignment is worth 2% of your overall course grade. 1. (2 marks, 0.5 each) What is the main or governing operator in each of the following formal statements? a) ¬(C ∨
D) b) ¬C & S c) (A & B) →
¬D d) A ∨
(B →
¬D) 2. (2 marks, 1 each) Translate each of the following sentences into formal notation. a) You can have FRIES or SALAD with your VEGGIE burger. c) SHARONA and CASSIE won't both go to the meeting unless it is on FRIDAY. 3. (4 marks, as indicated) Each of the following arguments is an instance of one of the following elementary argument forms: MP, MT, DN, Simp, Conj, CS, DS, or DeM. Which is it? a) (1 mark) Amy is not taking both calculus and physics this term. She is definitely taking calculus. It follows she is not taking physics. b) (1 mark) Amy is taking either physics or calculus this term. She is not taking physics this term. Therefore, she is taking calculus. c) (2 marks) If Amy is not taking calculus this term, she is taking physics this term. Amy is not taking physics this term. So, it is not the case that she is not taking calculus this term; which is to say, she is taking calculus this term. 4. (6 marks, 3 each) Prove the validity of the following abstract arguments, using the rules MP, MT, DN, Conj, Simp, CS, Disj, DS, DeM. a) (A v B) →
C, ¬C v D, ¬D ∴
¬B b) (G ∨
H) →
¬S, T →
M, ¬(M ∨
D), G & ¬L ∴
¬(S ∨
T) 5. (4 marks) Show that the following argument is valid by symbolizing it and then by giving a formal proof using any of the rules MP, MT, DN, Conj, Simp, CS, Disj, DS, DeM: If you eat apples and blueberries, you will not eat dessert. You will eat blueberries and dessert. Therefore, you will not eat apples. 6. (2 marks) Consider the following argument form: p →
q ∴
p →
(q & r) Show that it is invalid by finding an instance of that form that clearly has a true premise and a false conclusion. (Do not use examples from the text or your notes.)
