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Princeton PHI 201 - Practice Midterm Exam.

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PHI 201, Introductory Logic Spring 2005Practice Midterm Exam.1. Complete the following sentences.(a) An argument with premises φ1, . . . , φnand conclusion ψ is valid if ...(b) A sentence φ is inconsistent if ...2. Short answer: Explain, using words and/or pictures, the ∨-Elimination ruleof inference, including how dependency numbers are tabulated.3. Translate the following English sentences into sentence logic. Use the sug-gested letters for elementary sentences.(a) Fanny loves Edmund, but Edmund loves Miss Crawford. (F, E)(b) Fanny loves Mr. Crawford only if he helps her brother. (F, H)(c) If Fanny loves Mr. Crawford then Edmund is happy, unless Miss Craw-ford doesn’t love him. (F, E, M)4. Prove the validity of the following arguments. You may use any of the rulesof inference that we have learned.(a) 1. −P2. −Q / − (P ∨ Q)(b) 1. (P → Q) ∨ (P → R) / P → (Q ∨ R)5. Prove the following theorem. You may use any of the rules of inference thatwe have learned.// P ↔ (P & (Q ∨ −Q))6. Is the the following sentence a tautology, a contradiction, or a contingency?Justify your answer.(−A → A) → (B → (C → (D → (E → A))))7. True or false (justify your answer): There is an inconsistent sentence of theform φ → ψ, where φ is a contingency, and ψ is an arbitrary sentence.Practice Midterm Exam p. 1 of 2PHI 201, Introductory Logic Spring 20058. Does sentence (a) imply sentence (b)? Justify your answer.(a) (P ∨ Q) → (R ∨ S)(b) (P → R) ∨ (P → S)9. Is the English sentence connective “.. .because ... ” truth-functional? (e.g.,“The glass shattered because it was hit with a baseball.”) Justify your answer.10. Suppose that the sentence connective ◦ has the truth table given below:P Q P ◦ QT T FT F FF T FF F FFind an expression using only & , −, P, Q that is equivalent to P ◦ Q.11. True or False (explain and justify your answer): There could be a correctlywritten proof with the following line fragments (where n is some numbergreater than 1):1 (1) (P → Q) → Q A· · ·1 (n) − P → QPractice Midterm Exam p. 2 of


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