Kindly read the instructions 146 CHAPTER 6 ■ Propos it ional Log ic Which of the following propositions is a substitution instance of “p & q & q“? 1. The n

146

CHAPTER 6 â–  Propos it ional Log ic

Which of the following propositions is a substitution instance of “p & q & q“?

1. The night is young, and you’re so beautiful, and my flight leaves in thirty
minutes.

2. The night is young, and you’re so beautiful, and my flight leaves in thirty
minutes, and my flight leaves in thirty minutes.

3. You’re so beautiful, and you’re so beautiful, and you’re so beautiful.

Exercise II

For each of the following propositions, give three different propositional forms
of which that proposition is a substitution instance.

1. The night is young, and you’re so beautiful, and my flight leaves in thirty
minutes.

2. The night is young, and you’re so beautiful, and you’re so beautiful.

Exercise III

Indicate whether each of the following sentences expresses a propositional con-
junction or a nonpropositional conjunction—that is, whether or not it expresses
a conjunction of two propositions. If the sentence could be either, then specify a
context in which it would naturally be used to express a propositional conjunc-
tion and a different context in which it would naturally be used to express a
nonpropositional conjunction.

1. A monk married Devon and Nassier.
2. Fred had pie and ice cream for dessert.
3. The winning presidential candidate rarely loses both New York

and California.

Exercise IV

The proposition “The night is young, and you’re so beautiful” is a substitution
instance of which of the following propositional forms?

1. p

2. q

3. p & q
4. p & r

Exercise I

5. p & q & r
6. p & p
7. p or q

General Notes on the Chapter

Note #1: there’s lots of room for
extra practice on most of these
exercises, and I heartily encourage
you to do more! Learning logic is a
matter mostly of practice and
familiarity, and you can’t get that
from cramming. The best policy is
doing a little bit of logic every day –
even 20-30 min every day will work
wonders.

Note #2: the first major
obstacle with learning formal
logic is learning the procedure
of how to go about doing these
various tasks of analysis. If
you’re getting stuck in that way
where you don’t even know
how to begin, contact me
ASAP! 5 min on the phone
with me can save you hours of
frustration. I’m here to help
prevent those sorts of tragedies!

147

Bas ic Propos it ional Connect ives

Now we can look at an argument involving conjunction. Here is one that
is ridiculously simple:

Harry is short and John is tall.
Harry is short.

This argument is obviously valid. But why is it valid? Why does the conclusion
follow from the premise? The answer in this case seems obvious, but we will
spell it out in detail as a guide for more difficult cases. Suppose we