Download Quiz #1 KEY

 Your name: EMR 17: Deductive Logic Quiz #1 Due by 3 p.m. Remember: no notes, book, ipods, etc.! (14 questions, each worth ½ point.) 1. State our working definition of “validity”. An argument is valid if, and only if: It is not possible for all the premises to be true and the conclusion false. Note another common formulation: If the premises are all true, then the conclusion must be true (or: then the conclusion cannot be false). That formulation is not as clear, because the “scope” of that word “must” is itself unclear. One bad reading is this: Either the premises are not all true, or the conclusion must be false. Think about why that is a bad reading! 2. Suzy has an argument. It is valid. Its conclusion is true. So at least one of its premises must be true. Is this reasoning correct or incorrect? Explain. Incorrect. Consider: “All wombats enjoy the taste of chocolate; Ned is a wombat; therefore: Ned enjoys the taste of chocolate.” The argument is valid; the conclusion is true; both premises are false. In general, the only constraint that validity places on the actual truth or falsity of premises and conclusion is this: it cannot be that the premises are all true and the conclusion false. Thus, from the claim that Suzy’s argument is valid and has a true conclusion, nothing whatsoever follows about the truth or falsity of her premises. 3. Suzy has an argument with two premises. The argument is valid. The conclusion is false. What, if anything, can we conclude about the truth or falsity of the premises? (circle one) A. At least one premise is true. B. Both premises are true. C. At least one premise is false. D. Both premises are false. EMR 17 Quiz #1, fall 2015 1 E. Without more information, we cannot conclude anything about the truth of falsity of the premises. 4. Suzy has an argument with two premises. The argument is not valid. The conclusion is true. What, if anything, can we conclude about the truth or falsity of the premises? (circle one) A. At least one premise is true. B. Both premises are true. C. At least one premise is false. D. Both premises are false. E. Without more information, we cannot conclude anything about the truth or falsity of the premises. 5. Suzy has an argument. Two of its premises contradict each other (i.e., it is not possible for both of these premises to be true). What may we conclude about the validity of her argument? (circle one) A. It is not valid. B. It is valid. C. Without more information, we cannot tell whether it is valid. EMR 17 Quiz #1, fall 2015 2 6. Fill in the truth-­‐tables for the five connectives we have introduced: p
q
–p
p∨q
p.q
p⊃q
p≡q
T
T
⊥
T
T
T
T
T
⊥
⊥
T
⊥
⊥
⊥
⊥
T
T
T
⊥
T
⊥
⊥
⊥
T
⊥
⊥
T
T
7. Calculate the truth-­‐table for “(p ∨ q) . (–q ∨ –p)”. p
q
(p ∨ q) . (–q ∨ –p)
T
T
⊥
T
⊥
T
⊥
T
T
⊥
⊥
⊥
8. Calculate the truth-­‐table for “[(p . q) ∨ r] ≡ [(q . –r) ∨ p]”. p
q
r
[(p . q) ∨ r] ≡ [(q . –r) ∨ p]
T
T
T
T
T
T
⊥
T
T
⊥
T
T
T
⊥
⊥
⊥
⊥
T
T
⊥
⊥
T
⊥
⊥
⊥
⊥
T
⊥
⊥
⊥
⊥
T
EMR 17 Quiz #1, fall 2015 3 9. Calculate the truth-­‐table for “(p ⊃ q) ≡ (r ∨ –p)”. p
q
r
(p ⊃ q) ≡ (r ∨ –p)
T
T
T
T
T
T
⊥
⊥
T
⊥
T
⊥
T
⊥
⊥
T
⊥
T
T
T
⊥
T
⊥
T
⊥
⊥
T
T
⊥
⊥
⊥
T
Questions 10 – 13: Paraphrase, using “.”, “v”, and “–” as needed. In each case, state explicitly what English statement each statement-­‐letter (“p”, “q”, etc.) stands for. If you think more than one logically distinct paraphrase is defensible, give both, with an explanation of the ambiguity. 10. Even though he neither studied nor got a full night’s sleep, Billy aced the logic quiz. p: Billy studied q: Billy got full night’s sleep r: Billy aced the logic quiz Paraphrase: –p . –q . r EMR 17 Quiz #1, fall 2015 4 11. Billy either went to a movie or went to a play, but not both – unless Suzy joined him, in which case he did go to both. p: Billy went to a movie q: Billy went to a play r: Suzy joined Billy Paraphrase: (p . q . r) ∨ (p . –q . –r) ∨ (–p . q . –r) 12. Billy will ask Suzy on a date, although she will either refuse him or insist on limiting the date to coffee – unless he dresses much more stylishly than he has in the past, or apologizes for his earlier mistakes. p: Billy will ask Suzy on a date q: Suzy will refuse him r: Suzy will insist on limiting the date to coffee s: Billy will dress more stylishly t: Billy will apologize Paraphrase: p . (q ∨ r ∨ s ∨ t) 13. Billy hopes that either Suzy will go to the play with him, or that either Archibald or Randolph (but not both) will do so. Paraphrase: p (The expression “Billy hopes that” generates a non-­‐truth-­‐functional context.) 14. You are on the Island of Knights and Knaves. You meet three people, A, B, and C. A says, "B is the same as C." B says, "We are not all the same." What is the identity of each Islander? (circle the correct choice) A is a: Knight Knave B is a: Knight Knave C is a: Knight Knave EMR 17 Quiz #1, fall 2015 5