HOMEWORK #3

Propositional Logic I

(These exercises are adapted from Coppin 2004, §7.24.)

1. Use our formal propositional language that will be introduced in class (and that is adapted from the full first-order language in B&L, Ch. 2) to represent the following sentences. Be sure to give the syntax and semantics of your representation!
   1. I eat apples and pears.
   2. I eat apples and I eat pears.
   3. If I eat apples and pears, I usually like to take a walk.
   4. Every apple that I have ever eaten has been delicious.
   5. I eat apples only if I eat pears.
   6. There exists a book that lists all other books.
   7. If you haven't read the book that lists all other books, then you haven't read any book, unless you've read the book that lists books that do not exist, in which case you've read every book.
   8. John's father is tall.
   9. Mary believes that John's father is tall.
   10. It is possible that John will be tall when he grows up.

2. Construct truth tables, showing truth values for all subpropositions, using the notation to be introduced in class, for the following propositions:
   1. (¬P ^ (P v Q))
   2. ((¬P ^ (P v Q)) ^ (¬Q v R))

3. As in problem 1, above, represent the following sentences in our propositional language; give your syntax and semantics.
   1. If you go to Mexico, you will be far away.
   2. I cannot hear you when you are far away.
   3. When I can't hear you, I forget what you look like.
   4. If I come to Mexico, and I don't know what you look like, I won't be able to find you.
   5. If you go to Mexico, and I follow you, I won't be able to find you.