1. a. If you do not overtrain, then you will be able to meet the standard.
This states a sufficient condition.
b. A conjunction is true only if one of its conjuncts is true, but it is not the case that if only one of its
conjuncts is true then it is true.
This (obviously) states a condition that is necessary but not sufficient.
c. Stage one: I will meet you at the train station if traffic is not bad, and in the case that traffic is bad I will
not meet you.
Stage two: If traffic is not bad, I will meet you at the train station, and if traffic is bad I will not meet you.
This states a strong exception.
2. a. W – I will go to Boston
R – It rains
B – Bill will go to Boston
C – Bill’s car is running
Stage one: I will not go to Boston if it does not rain, although Bill will go if and only if his car is running.
Stage two: If it does not rain I will not go to Boston, although Bill will go if and only if his car is running.
(~R ⊃ ~W) & (B ≡ C)
b. M – Mares eat oats
B – Bears eat oats
L – Little lambs eat ivy
(M & B) & L
c. W – William fancied that leprechauns or poltergeists were persecuting him.
(This sentence is not a truth-functional compound because “fancied that” is not a truth functional
connective and trying to make the “or” the main connective by breaking the sentence down into “either
William fancied that leprechauns were persecuting him or etc” does not produce a truth-functionally
d. C – Michael Crichton is one of the most creative people alive
T – Michael Crichton tries his hand at television
S – Michael Crichton will be a success.
C & (T ⊃ S)
e. T – Two heads are better than one.
3. Only the first sentence is not already in standard form. It is rewritten as, “If the local bookstore does
not carry novels by Mishima, I won’t be able to complete my bibliography.
B – The local books