3.1.xa. Exercise answers
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)
H: the soup was hot; K: the soup was thick; O: the soup was too thick; T: the soup was too hot
both both H and not T and both K and not 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
H: the equipment is here; S: the equipment is likely to arrive soon
both not H and not 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
A: someone answered the phone; R: the phone rang 10 times
both not A and 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
A: the alarm must have gone off; H: Ted heard something
both A and not 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)
B: they will stay within the budget; D: they will meet the deadline
not both D and 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
B: they will stay within the budget; D: they will meet the deadline
both not D and 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
B: they will stay within the budget; D: they will meet the deadline
both not D and not B
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h. |
Tod shut off the alarm ∧ ¬ Tod woke up
A ∧ ¬ W
A: Tod shut off the alarm; W: Tod woke up
both A and not W
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i. |
¬ they will meet the deadline without going over the budget ¬ (they will meet the deadline ∧ ¬ they will go over the budget)
¬ (D ∧ ¬ G)
D: they will meet the deadline; G: they will go over the budget
not both D and not G
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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)
both J and not both J and not 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)
both A and both not B and not C
A: Ann liked the movie; B: Bill liked the movie; C: Carol liked the movie
The alternative (and equivalent) analysis as A ∧ ¬ E (where 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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b. |
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c. |
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