| 1. |
Analyze the sentence below in as much detail as possible. Be sure that the unanalyzed components of your answer are complete and independent sentences and that you respect any grouping in the English.
Either Bob didn’t call or neither Alice nor Carol was home
answer
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| 2. |
Synthesize an idiomatic English sentence expressing the proposition which is assigned to the symbolic form below by the intensional interpretation to its right—i.e., give an English sentence whose analysis would be the following:
P ∧ ¬ (S ∧ V)
P: Ralph went to Portland; S: Ralph went to Seattle; V: Ralph went to Vancouver
answer |
| Check each of the following claims of entailment. Do not use detachment or attachment rules. If a derivation fails, present a counterexample that divides an open gap. | ||
| 3. |
A ∧ ¬ B ⊨ ¬ (B ∧ C)
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| 4. |
A ∧ ¬ B, B ∨ C ⊨ A ∧ C
answer |
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| 5. |
¬ (A ∧ ¬ B) ⊨ A ∨ B
answer |
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| 6. |
[This question was on a topic not covered in F08]
Use a series of replacements to show the following:
¬ A ∧ ¬ (B ∧ C) ≃ ¬ (A ∨ B) ∨ ¬ (A ∨ C)
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| 3. |
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| 5. |
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| 6. |
[This question was on a topic not covered in F08]
¬ A ∧ ¬ (B ∧ C)
≃ ¬ A ∧ (¬ B ∨ ¬ C) ≃ (¬ A ∧ ¬ B) ∨ (¬ A ∧ ¬ C) ≃ ¬ (A ∨ B) ∨ ¬ (A ∨ C) |