CSCI 1323 (Discrete Structures), Spring 2002:
Homework 2

Assigned:

January 29, 2002.

Due:

February 7, 2002, at the start of class.

Credit:

20 points.

Problems

Do the following problems. You do not need to turn in answers for the ones marked ``Not to turn in''. Most such problems will be those for which the textbook provides an answer in the back of the book, so you can check your work.

1. (Not to turn in.) Do problem 2, parts (c) and (d), on p. 41 of the textbook.

2. (4 points) Do problem 2, parts (e), (f), (g), and (h), on p. 41 of the textbook.

3. (Not to turn in.) Do problem 4, part (a), on p. 41 of the textbook.

4. (Not to turn in.) Do problem 6, parts (a) and (b), on p. 42 of the textbook.

5. (Not to turn in.) Do problem 9, parts (a) and (b), on p. 42 of the textbook.

6. (6 points) Using the predicate symbols shown and appropriate quantifiers, write each English-language statement as a predicate wff. (The domain is the whole world.)

   $W(x)$ is ``$x$ is a positive integer.''
   $P(x)$ is ``$x$ is prime.''
   $G(x, y)$ is ``$x \ge y$.''

   • Some positive integers are prime.
   • Not all positive integers are prime.
   • For every positive integer $n$, there is a positive integer $m$ such that $m$ is prime and $m \ge n$.
   • There is a largest prime.

7. (Not to turn in.) Do problem 16, part (a), on p. 41 of the textbook.

8. (Not to turn in.) Do problem 2 on p. 56 of the textbook.

9. (Not to turn in.) Do problem 4 on p. 56 of the textbook.

10. (Not to turn in.) Do problem 9 on p. 56 of the textbook.

11. (4 points) Do problem 11 on p. 57 of the textbook.

12. (6 points) Do problem 12 on p. 57 of the textbook.

13. (Not to turn in.) Do problem 17 on p. 57 of the textbook.

14. (Not to turn in.) Do problem 22 on p. 57 of the textbook.