| 1. | Analyze each of the following sentences in as much detail as possible. | |
| a. | The soup was hot but not too hot, and thick but not too thick. | |
| b. | The equipment isn’t here and it’s unlikely to arrive soon. | |
| c. | No one answered the phone even though it rang 10 times. | |
| d. | The alarm must have gone off, but Ted didn’t hear anything. | |
| e. | They won’t both meet the deadline and stay within the budget. | |
| f. | They won’t meet the deadline, but they will stay within the budget. | |
| g. | They won’t meet the deadline, and they won’t stay within the budget. | |
| h. | Tod shut off the alarm without waking up. | |
| i. | They won’t meet the deadline without going over the budget. | |
| j. | Larry joined in, but not without being coaxed. | |
| k. | Ann liked the movie, but neither Bill nor Carol did. | |
| 2. | Restate each of the forms below, putting English notation into symbols and vice versa. Indicate the scope of connectives in the result by underlining. | |
| a. | ¬ ¬ (A ∧ B) | |
| b. | ¬ (¬ A ∧ B) | |
| c. |
both not A and both not B and C
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| d. |
both not both A and B and not C
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| 3. | Synthesize idiomatic English sentences that express the propositions associated with the logical forms below by the intensional interpretations that follow them. | |
| a. |
C ∧ ¬ F
[C: it was cold; F: there was frost] |
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| b. |
¬ S ∧ (H ∧ I)
[H: Sue heard a crash; I: Sue went to investigate; S: someone saw the accident] |
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| c. |
(D ∧ N) ∧ ¬ P
[D: it was a design; N: it was new; P: it pleased someone] |
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| d. |
¬ (I ∧ N)
[I: we’ll win in Iowa; N: we’ll win in New York] |
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| e. |
¬ I ∧ N
[I: we’ll win in Iowa; N: we’ll win in New York] |
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| f. |
¬ (I ∧ ¬ L)
[I: we’ll win in Iowa; L: we’ll lose in New York] |
| 4. | Calculate truth values for all components of the forms below using the extensional interpretation provided in each case. | ||||||||||||||||||||||
| a. |
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| b. |
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| c. |
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