3.1.x. Exercise questions

1. Analyze each of the following sentences in as much detail as possible.
  a. The soup was hot but not too hot, and thick but not too thick.
  b. The equipment isn’t here and it’s unlikely to arrive soon.
  c. No one answered the phone even though it rang 10 times.
  d. The alarm must have gone off, but Ted didn’t hear anything.
  e. They won’t both meet the deadline and stay within the budget.
  f. They won’t meet the deadline, but they will stay within the budget.
  g. They won’t meet the deadline, and they won’t stay within the budget.
  h. Tod shut off the alarm without waking up.
  i. They won’t meet the deadline without going over the budget.
  j. Larry joined in, but not without being coaxed.
  k. Ann liked the movie, but neither Bill nor Carol did.
2. Restate each of the forms below, putting English notation into symbols and vice versa. Indicate the scope of connectives in the result by underlining.
  a. ¬ ¬ (A ∧ B)
  b. ¬ (¬ A ∧ B)
  c. both not A and both not B and C
  d. both not both A and B and not C
3. Synthesize idiomatic English sentences that express the propositions that are associated with the logical forms below by the intensional interpretations that follow them.
  a. C ∧ ¬ F
C: it was cold; F: there was frost
  b. ¬ S ∧ (H ∧ I)
H: Sue heard a crash; I: Sue went to investigate; S: someone saw the accident
  c. (D ∧ N) ∧ ¬ P
D: it was a design; N: it was new; P: it pleased someone
  d. ¬ (I ∧ N)
I: we’ll win in Iowa; N: we’ll win in New York
  e. ¬ I ∧ N
I: we’ll win in Iowa; N: we’ll win in New York
  f. ¬ (I ∧ ¬ L)
I: we’ll win in Iowa; L: we’ll lose in New York
4. Complete the following truth tables. That is, calculate truth values for all components of the forms below using the extensional interpretation provided on the left in each case.
  a.
ABCA∧¬(B∧C)
TFF
  b.
ABCA∧(¬B∧C)
TFF
  c.
ABCD(¬A∧¬B)∧(¬(A∧C)∧D)
FTTT

For more exercises, use the exercise machine.

Glen Helman 16 Jul 2012