Math 511: Test 1
October 21, 2013
Question:
1
2
3
4
5
6
Total
Points:
9
9
7
9
9
9
52
Score:
1. (9 points) Let A and B be the following subsets of R2 :
A = (x, y )
y = x2 + 1
B = (x, y )
y = 2x2
(a) Find all elements in A B .
(b) Find an element in A B c .
Math 511: Test 2
November 25, 2013
Question:
1
2
3
4
5
6
7
Total
Points:
8
8
8
8
8
8
2
50
Score:
1. (8 points) Let A and B be denumerable sets with A B = .
(a) Without using cardinal arithmetic, show that A B is denumerable.
(b) Use cardinal arithmetic to
Math 511: Test 2 Review (updated from Fall 12)
Let R denote the real numbers, Q the rationals, Z the integers, and P the positive integers.
1. Create or describe an explicit bijection between the following sets:
(a) Z cfw_. . . , .001, .01, .1, 1, 10, 100
Math 511: Test 2 Review Partial Solutions
1. Create or describe an explicit bijection between the following sets:
(a) n 10n
(b) n the n-th prime number; e.g. 1 2, 2 3, 3 5, 4 7, 5 11, . . .
(c) One possible example is 1 Manhattan, 2 Bronx, 3 Queens, 4 Bro
Math 511: Test 1 Review
1. Let A and B be the following subsets of R2 :
A = (x, y )
y = x2 + 1
B = (x, y )
y = 2x
(a) List all elements in A B .
(b) Show that A
B.
2. Consider the function f (x) =
x2 1.
(a) What is the domain and target of f ?
(b) Is f on
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HOMEWORK 4 - DUE 10/7/2013
MATH 511
If you did not do problems 6-9 on HW3, do them for this homework.
(1) Consider the relation 5 on Z dened by:
a 5 b t Z such that a = b + 5t.
We have already shown this is an equivalence relation. We will denote the quot
Math 511: Final Exam
December 17, 2012
Question:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Total
Points:
8
6
6
10
10
8
6
4
9
9
4
10
6
4
100
Score:
1. (8 points) Let S and T be the following subsets of R2 :
S = (x, y )
y = x2 + 1
T = (x, y )
y = 2x
(a) Find an elem