| Phi 270 Fall 2013 |
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4.1.x. Exercise questions
| 1. | Analyze each of the following sentences in as much detail as possible. | |
| a. | Either Tommy ate his vegetables or he didn’t get any dessert. | |
| b. | Mike heard neither the phone nor the doorbell. | |
| c. | Either Mike wasn’t home or he wasn’t answering the phone. | |
| d. | The package was sent, but either it’s still on its way or it’s been lost in the mail. | |
| e. | Neither the House nor the Senate had acted on the bill, but the White House expressed confidence that it would pass. | |
| f. | Sam won’t pass through without either stopping by or calling. | |
| g. | Either Davis or Edwards will take you or give you directions. | |
| h. | We’ll have either a can without an opener or an opener without a can. | |
| i. | Neither Jan nor Ken had matches or a lighter. | |
| j. | Both Ann and Bill were in town but neither knew the other was. | |
| k. | Either Tom, Dick, or Harry will handle both the scheduling and the publicity. | |
| l. | The scheduling will be handled by either Tom, Dick, or Harry—as will the publicity. | |
| 2. | Restate each of the following forms, putting English notation into symbols and vice versa. Indicate the scope of connectives in the result by underlining. | |
| a. | A ∧ (B ∨ C) | |
| b. | (A ∧ B) ∨ C | |
| c. |
not either A or not B
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| d. |
both either A or B and either A or 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. |
B ∨ N B: it was the butler; N: it was the nephew |
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| b. |
¬ (A ∨ S) A: the alarm worked; S: the sprinkler worked |
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| c. |
¬ A ∨ ¬ P A: the part arrived; P: the part was the problem |
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| d. |
A ∨ ¬ (B ∧ C) A: Ann has a large car; B: Bill will ride with us; C: Carol will ride with us |
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| e. |
(R ∨ D) ∧ W D: there was a heavy dew; R: it rained over night; W: it is wet |
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| f. |
(A ∧ Z) ∨ (F ∧ ¬ (A ∨ Z)) A: AAA ∧ Co. will profit from the deal; F: the deal will fall through; Z: ZZZ Inc. will profit from the deal |
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For more exercises, use the exercise machine.