2.1.xa. Exercise answers
| 1. | a. |
Mike visited London ∧ Mike visited Paris
L ∧ P
L: Mike visited London; P: Mike visited Paris |
| b. |
Ann wanted white wine ∧ Bill and Carol wanted red wine Ann wanted white wine ∧ (Bill wanted red wine ∧ Carol wanted red wine)
A ∧ (B ∧ C)
A: Ann wanted white wine; B: Bill wanted red wine; C: Carol wanted red wine |
| c. |
It will rain and clear off ∧ it will rain (it will rain ∧ it will clear off) ∧ it will rain
(R ∧ C) ∧ R
C: it will clear off; R: it will rain |
| d. |
That is a market ∧ that is new relative to other markets but growing That is a market ∧ (that is new relative to other markets ∧ that is growing)
M ∧ (N ∧ G)
G: that is growing; M: that is a market; N: that is new relative to other markets |
| e. |
Confucius is affable but dignified ∧ Confucius is austere but not harsh ∧ Confucius is polite but completely at ease (Confucius is affable ∧ Confucius is dignified) ∧ (Confucius is austere ∧ Confucius is not harsh) ∧ (Confucius is polite ∧ Confucius is completely at ease)
(A ∧ D) ∧ (S ∧ H) ∧ (P ∧ E)
A: Confucius is affable; D: Confucius is dignified; E: Confucius is completely at ease; H: Confucius is not harsh; P: Confucius is polite; S: Confucius is austere |
| f. |
Tim lost his glasses and his wallet ∧ Tim’s glasses and wallet were each returned (Tim lost his glasses ∧ Tim lost his wallet) ∧ (Tim’s glasses were returned ∧ Tim’s wallet was returned)
(G ∧ W) ∧ (R ∧ T)
G: Tim lost his glasses; R: Tim’s glasses were returned; T: Tim’s wallet was returned; W: Tim lost his wallet |
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| g. |
Tim lost his glasses and his wallet ∧ one person found both Tim’s glasses and his wallet (Tim lost his glasses ∧ Tim lost his wallet) ∧ one person found both Tim’s glasses and his wallet
(G ∧ W) ∧ O
G: Tim lost his glasses; O: one person found both Tim’s glasses and his wallet; W: Tim lost his wallet Note: One person found both Tim’s glasses and his wallet cannot be analyzed further because One person found Tim’s glasses ∧ one person found Tim’s wallet does not imply that the same person found both. |
| 2. | a. | A ∧ (B ∧ C) |
| b. | (A ∧ B) ∧ C |
| c. |
both both A and B and both C and D
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| d. |
both A and both both B and C and D
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| e. |
both both A and both B and C and D
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| f. | ((A ∧ B) ∧ C) ∧ D |
| 3. | a. |
(Fred visited Venice ∧ Fred visited Florence) ∧ Fred spent a week in Rome Fred visited Venice and Florence ∧ Fred spent a week in Rome Fred visited Venice and Florence, and he spent a week in Rome |
| b. |
(he was a judge ∧ (he was stern ∧ he was fair)) ∧ he had an excellent knowledge of the law (he was a judge ∧ he was stern but fair) ∧ he had an excellent knowledge of the law He was a stern but fair judge who had an excellent knowledge of the law |
| c. |
(we arrived cold ∧ we arrived tired ∧ we arrived hungry) ∧ (we left warm ∧ we left stuffed ∧ we left sleepy) We arrived cold, tired, and hungry ∧ we left warm, stuffed, and sleepy We arrived cold, tired, and hungry; and we left warm, stuffed, and sleepy |
| d. |
Old King Cole was a merry old soul ∧ Old King Cole was a merry old soul Old King Cole was a merry old soul, and a merry old soul was he |
| 4. | Numbers below the tables indicate the order in which values were computed | |||||||||||||||||||||||||
| a. |
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| b. |
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