## Fall 2003

## Homework Assignments

8/28 pp15-16: 12, 14, 16, 17, 19, 21, 23, 25.

9/2 p16: 27, 29, 37, 38, 43, 46; pp27-28: 3, 5, 9, 12, 13.

9/4 p55: 5, 7, 9, 11, 13, 16, 18.

9/9 pp242-243: 7, 8, 14, 15

9/11 pp242-243: 5, 6, 10, 13, 18

9/16 pp87-88: 4, 6, 9, 11, 20; pp97-98: 3, 5, 13, 16, 22, 31, 33;
p257: 9, 10, 28

9/18 Karnaugh Map Handout: 1, 3, 4, 5, 6, 9, 10, 11, 12

10/2 pp204-205: 6, 9, 12, 14; p211: 8, 14 (#14 on p205 is extra
credit)

10/7 Prove the Associative, Identity, and Commutative properties
for addition of natural numbers. Also prove the left and right
Distributive properties. You may use induction.

10/9 Prove the Commutative, Associative, and Identity Properties
of multiplication of natural numbers.

Find quotients and remainders for the following division problems.

7/3, 3/7, 112/15, 1001/7

10/14 p178: 12, 13, 14

10/16 pp138-139: 29, 31.

10/21 Reduce the following fractions using products of primes.
142857/999999, 769230/999999, 90243/99999, 8487/99999

10/28 p153: 14, 15, 17, 18, 19, 23, 25, 26.

11/11 pp354-355: 1, 3, 4, 6, 12; pp368-369: 5, 7, 15, 17.

11/13 pp384-385:1, 2, 5, 10; pp410-411: 1, 8, 20.

11/18 1. State the definition for a function to be one to one.

2. State the definition for a function tobe onto.

3. Prove that the composition of two one to one functions is one
to one.

4. Prove that the composition of two onto functions is onto.

5. Prove that the composition of two one to one correspondences is
a one to one correspondence.

11/20 Prove that if f is a one to one correspondence then so is f
inverse.

p411: 15, 16, 17, 18; pp544-545: 1, 3, 4, 8; p554: 1, 3, 6, 12,
21.

pp570-571: 1, 2, 4, 6, 8, 14, 19, 20, 27, 28, 29. Prove that a
partition induces an equivalence relation on a set by defining two
elements to be related if they are in the same subset of the
partition.

11/25 Prove: Let A be a set with a partition. The relation induced
by the partition is an equivalence realtion.

p570: 1, 2, 4, 6, 8, 14, 19, 20, 27, 28, 29.

12/2 p423: 14, 15, 16, 17.