Download CS323: Assignment 1

CS 3630: Assignment 1
(10 points)
Due Wednesday (week 2), February 1, by noon
Name:
Section: 1 (9 AM) 2 (10 AM)
Save a copy of the file and name it as UserName_A1.doc(x). For example, YangQ_A1.
Complete your UserName_A1 file and drop it to the following folder by the due time:
K:\Courses\CSSE\yangq\CS3630\1Dropbox
Follow the style given in the class. For example,
A = {1, 2, 3, 4}
You may lose two points on style, including the file name and your name with section number.
1. (2 points) Give the following sets by listing all elements in the sets.
1.1. All odd numbers between 0 and 13, inclusive.
1.2. All courses you are taking this semester.
2. (2 points)
2.1 Give two finite, non-empty sets A and B, satisfying the following condition:
A  B and A  B = A
2.2 Give two finite, non-empty sets A and B, satisfying the following condition:
|A  B| = |A| + |B|
2.3 Give two finite, non-empty sets A and B, satisfying the following condition:
|A| > |B| > |A  B| > 0
2.4 Give three finite, non-empty sets A, B, and C, satisfying the following condition:
A  B  C = , but
A  B  , A  C  , and B  C  
3. (2 points) Give the power set of Z = {1, 2, 3}.
4. (2 points) Given the following two sets:
A = {u, v}
B = {5, 10}
4.1 Give the Cartesian Product of A and B (list all tuples).
4.2 Give the Cartesian Product of B and A (list all tuples).
4.3 Give the Cartesian Product of the three sets A, B and A (list all tuples).
4.4 List all tuples of the following relation:
R = {(a, b, c): (a, b, c)  A  B  A and b = 10}
5. (2 points) Given the two sets below:
X = {x: x = 5 * n, where n  N}
Y = {y: y = (7 * n) - 2, where n  N}
Note: set N is the set of all non-negative integers.
5.1. List the first three elements of each set, starting with the smallest one.
5.2. Give a one-to-one mapping between the two sets. The formula must not contain n.