Homework for Philosophy 270, Fall 2006
Answer to homework on §3.1
(i) analyze the following in as much detail as possible using conjunction and negation, and state the result using both symbolic and English notation:
Although Al saw the problem and reported it, he was able to work around it.
Ann and Bill didn’t both call; and, while Ann heard the news, Bill didn’t
Ann and Bill didn’t both call
∧
while Ann heard the news, Bill didn’t
¬
Ann and Bill both called
∧
(Ann heard the news
∧
Bill didn’t hear the news)
¬
(
Ann called
∧
Bill called
)
∧
(
Ann heard the news
∧
¬
Bill heard the news
)
¬ (C ∧ L) ∧ (H ∧ ¬ R)
both
not
both C and L
and
both
H
and
not R
C: Ann called; H: Ann heard the news; L: Bill called; R: Bill heard the news
(ii) synthesize a sentence with the following form using the intensional interpretation given after it:
I ∧ ¬ P
I: Ann influenced the vote; P: Ann was present
Ann influenced the vote ∧ ¬ Ann was present
Ann influenced the vote ∧ Ann wasn’t present
Ann influenced the vote, and Ann wasn’t present
or: Ann influenced the vote even though she wasn’t present
or: Ann influenced the vote but wasn’t present
or: Ann influenced the vote without being present