Translating Passages


Translate each passage into formal notation. This will involve first, identifying the simple statements and assigning a letter to each; and second, putting the simple ststements together in the right way with statement operators and grouping symbols. If the passage is an argument, you need to identify the conclusion and symbolize it correctly too.



1. This steak is tender only if it's fatty, and if it's fatty then it's not good for me. I won't eat it unless it's good for me. Therefore, I won't eat this steak. [solution]


2. The wheat will grow well only if there is enough rain and it neither hails nor gets too hot. Only if it gets too hot if and only if it does not hail will the tomatoes grow well. Therefore, the wheat and the tomotoes will not both grow well. [solution]


3. The bank is open and the laundry is not closed. If the restaurant is open, then the laundry is closed. Either the restaurant or the garage is open, but not both. The laundry is not closed only if the tailor is open. If the bank is closed, the tailor is closed. Therefore, either the tailor is open or the garage is closed. [solution]


4. Ross will argue with Rachel if either Rachel takes too long or Joey doesn't get ready. If Chandler and Joey don't get ready, then the taxi will leave unoccupied. But the taxi will not leave unoccupied. Therefore, if Chandler gets ready then Ross won't argue with Rachel. [solution]


5. The yellow substance is an acid, if and only if, if it reacts with a base then a salt it produced. If a salt is produced, then either the yellow substance is an acid, or both the yellow substance is a base and the experiment is flawed. The experiment is not flawed and the yellow substance is not a base. Furthermore, and salt is produced. Therefore, the yellow substance is an acid. [solution]