| 1. |
Analyze the sentence below in as much detail as possible and express the result in both symbolic and English notation. Be sure that the unanalyzed components of your answer are complete and independent sentences and try to respect any grouping in the original sentence.
Sam didn't both find the problem and fix it, but either it went away on its own or there was no problem to begin with
[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:
¬ (D ∨ M) ∧ H
[D: Al had directions; H: Al made it home; M: Al had a map]
[answer] |
| Check each of the following claims of entailment. Do not use attachment rules but you may use detachment rules. If a derivation fails, present a counterexample that divides its premises from its conclusion. | ||
| 3. |
¬ B ⇒ ¬ (A ∧ (B ∧ C))
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| 4. |
A ∨ B ⇒ C ∨ B
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| 5. |
Use derivations to show the following entailment. You may use attachment rules and using them may make the derivation somewhat shorter.
¬ ((A ∨ B) ∧ ¬ C), A ⇒ C
[answer]
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| 6. |
[This question was on a topic not covered in F05]
Use a series of replacements to show the following:
¬ (A ∨ (B ∧ C)) ⇔ ¬ (A ∨ B) ∨ (¬ A ∧ ¬ C)
[answer]
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| 3. |
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| 5. |
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OR |
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| 6. |
[This question was on a topic not covered in F05]
¬ (A ∨ (B ∧ C))
⇔ ¬ A ∧ ¬ (B ∧ C) ⇔ ¬ A ∧ (¬ B ∨ ¬ C) ⇔ (¬ A ∧ ¬ B) ∨ (¬ A ∧ ¬ C) ⇔ ¬ (A ∨ B) ∨ (¬ A ∧ ¬ C) |