| 1. | a. |
The soup was hot but not too hot ∧ the soup was thick but not too thick
(the soup was hot ∧ the soup was not too hot) ∧ (the soup was thick ∧ the soup was not too thick) (the soup was hot ∧ ¬ the soup was too hot) ∧ (the soup was thick ∧ ¬ the soup was too thick)
(H ∧ ¬ T) ∧ (K ∧ ¬ O)
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| b. |
The equipment isn’t here ∧ the equipment is unlikely to arrive soon
¬ the equipment is here ∧ ¬ the equipment is likely to arrive soon
¬ H ∧ ¬ S
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| c. |
No one answered the phone ∧ the phone rang 10 times
¬ someone answered the phone ∧ the phone rang 10 times
¬ A ∧ R
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| d. |
The alarm must have gone off ∧ Ted didn’t hear anything
The alarm must have gone off ∧ ¬ Ted heard something
A ∧ ¬ H
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| e. |
¬ they will both meet the deadline and stay within the budget
¬ (they will meet the deadline ∧ they will stay within the budget)
¬ (D ∧ B)
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| f. |
They won’t meet the deadline ∧ they will stay within the budget
¬ they will meet the deadline ∧ they will stay within the budget
¬ D ∧ B
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| g. |
They won’t meet the deadline ∧ they won’t stay within the budget
¬ they will meet the deadline ∧ ¬ they will stay within the budget
¬ D ∧ ¬ B
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| h. |
Tod shut off the alarm ∧ ¬ Tod woke up
A ∧ ¬ W
|
| i. |
¬ they will meet the deadline without going over the budget
¬ (they will meet the deadline ∧ ¬ they will go over the budget)
¬ (D ∧ ¬ G)
|
| j. |
Larry joined in ∧ Larry did not join in without being coaxed
Larry joined in ∧ ¬ Larry joined in without being coaxed Larry joined in ∧ ¬ (Larry joined in ∧ ¬ Larry was coaxed)
J ∧ ¬ (J ∧ ¬ C)
[C: Larry was coaxed; J: Larry joined in]
This is equivalent to J ∧ ¬ ¬ C and also to J ∧ C, but the analysis shown is closer to the form of the English. |
| k. |
Ann liked the movie ∧ neither Bill nor Carol liked the movie
Ann liked the movie ∧ (¬ Bill liked the movie ∧ ¬ Carol liked the movie)
A ∧ (¬ B ∧ ¬ C)
[A: Ann liked the movie; B: Bill liked the movie; C: Carol liked the movie]
The alternative analysis as A ∧ ¬ E [E: either Bill or Carol liked the movie] is closer to the English but it is less satisfactory because it displays less structure. The next chapter will give us the means carry this sort of analysis further by analyzing E as a compound of B and C. |
| 2. | a. |
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| b. |
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| c. |
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| d. |
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| 3. | a. |
It was cold ∧ ¬ there was frost
It was cold ∧ there was no frost It was cold, but there was no frost |
| b. |
¬ someone saw the accident ∧ (Sue heard a crash ∧ Sue went to investigate)
No one saw the accident ∧ Sue heard a crash and went to investigate No one saw the accident, but Sue heard a crash and went to investigate |
| c. |
(it was a design ∧ it was new) ∧ ¬ it pleased someone
It was a new design ∧ it pleased no one It was a new design, and it pleased no one |
| d. |
¬ (we’ll win in Iowa ∧ we’ll win in New York)
¬ (we’ll win in both Iowa and New York) We won’t win in both Iowa and New York |
| e. |
¬ we’ll win in Iowa ∧ we’ll win in New York
We won’t win in Iowa ∧ we’ll win in New York We won’t win in Iowa, but we’ll win in New York |
| f. |
¬ (we’ll win in Iowa ∧ ¬ we’ll lose in New York)
¬ (we’ll win in Iowa without losing in New York) We won’t win in Iowa without losing in New York |
| 4. | Numbers below the tables indicate the order in which values were computed. | |||||||||||||||||||||||||||||||||||||||||||||||||
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| c. |
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