Exercises for propositional logic i  (Page 2/5)

[Practice problem $—$ solution provided.]

While the following argument may sound plausible initially, give a particular situation where the conclusion doesn't hold (eventhough the premises do). Then, in a sentence or two, sketch why your counterexamplemay still represent rational behavior by pointing out a real-worldsubtlety that the initial argument ignored.

1. If a certain outfit meets a dress code, then per force all less-revealing outfits also meet that dress code.

2. In public transportation projects, out of two alternatives,the cheaper one which gets the job done is the better choice.

Choose just one of the following informal arguments. While the argument sounds plausible initially,give a particular situation where the conclusion doesn't hold (even though the premises do).Then, briefly state why your counterexample may still represent rational behavior by pointing out a real-worldsubtlety that the initial argument ignored.

1. [cell phone] Talking on a cell phone while drivingincreases the likelihood of an accident. Interestingly, hands-free phones do not significantly help . It's just the distraction of a phone conversationthat causes the problem.

2. [equivalent products] If two companies offer two materially equivalent products,then most everybody will buy the cheaper one.

3. [service] In a free market,if a company doesn't offer good service, individual customers will become fed up and take their businesselsewhere.

4. [web browser] If there are two versions of a free web browser,and they run equally quickly, users will use the one with better features/interface.

5. [door-locking] Anybody who really wants to break into your house while you're gonewill be able to. (For instance, using a towel to muffle sound,break the corner of a back window, reach in and unlatch the window, and climb through.)So there's no point in locking your front door.

[Practice problem $—$ solution provided.]

Let $p$ , $q$ , and $r$ be the following propositions:

• $p$ : You get an A on the final exam
• $q$ : You do every exercise in the book.
• $r$ : You get an A in this class.

1. You get an A in this class, but you do not do every exercise in the book.

2. To get an A in this class, it is necessary for you to get an A on the final.

3. Getting an A on the final and doing every exercise in the book is sufficient for getting an A in this class.