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
  d. both either A or B and either A or C
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
  b. ¬ (A ∨ S)
A: the alarm worked; S: the sprinkler worked
  c. ¬ A ∨ ¬ P
A: the part arrived; P: the part was the problem
  d. A ∨ ¬ (B ∧ C)
A: Ann has a large car; B: Bill will ride with us; C: Carol will ride with us
  e. (R ∨ D) ∧ W
D: there was a heavy dew; R: it rained over night; W: it is wet
  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

For more exercises, use the exercise machine.

Glen Helman 11 Jul 2012