Math 2000: Set Theory
Assignment 5
Due Date: Oct. 22 2012
Problem 1. Let a, b Z. Prove that if a|b and b|c then a|c.
Proof. If a|b and b|c then there exist integers p, q such that b = pa and c = qb. Subbing the former into the
latter, we obtain c = q(pa)
Math 2000: Set Theory
Assignment 4
Due Date: Oct. 15 2012
Problem 1. Solve x2 |x| 2 < 0 in terms of allowable intervals of values x.
Proof. First, let x 0. We then have x2 x 2 = (x 2)(x + 1) < 0. The only way the product of two
numbers is negative is if o
Math 2000: Set Theory
Assignment 6
Due Date: Oct. 29 2012
Problem 1. Let n N (n 5) and suppose that n and n + 2 are both prime (pairs of prime numbers like
this are called twin primes). Prove that n = 6k 1 for some k N.
Solution: n can not be even because
Math*2000: Set Theory
Assignment 2
Due Date: Sept. 24 2012
Problem 1. Using the laws of the algebra of propositions and the rules of inference prove that
P Q, R S, (Q S), R
P
is a valid argument.
Proof. 1. P Q
2. R S
3. (Q S)
4. R
5a. S (from 4 and 2 by M
Math 2000: Set Theory
Assignment 3
Due Date: Oct. 1 2012
Problem 1. Let A, B, C be sets. Determine if the following assertions are true or false. Provide a proof or
counterexample in each case.
a) (A B) (B C) A B
b) (A B) (B C) A B
Proof. a) False. Take a
MATH*2000 Fall 2012 Lab #2
Thursday, September 20
Problem 0.1. Test the validity of the following argument:
If I study, then I will not fail Math 2000.
If I do not play X-box games, then I will study.
But I failed Math 2000.
Therefore I must have not play
Math*2000: Set Theory
Assignment 1
Due Date: Sept.17 2012
Problem 1. Negate the following sentences.
1. I am not inside.
2. If it rains, Ill get wet.
3. If I study a lot and I work hard, Ill get a good grade in Math 2000.
4. I like eating pizza and I driv
MATH*2000 Fall 2012 Lab #4
Thursday, October 4
Problem 0.1. Compute each of the following.
1. |P(A)|, where A = cfw_Wednesdays in September 2012.
2. |P(A)|, where A = cfw_x N | x3 + 2 = 29.
3. |P(A B)|, where A = cfw_x N | x is prime and B = cfw_x N |x is
MATH*2000 Fall 2012 Lab #3
Thursday, September 27
Problem 0.1. An identity for an operation (such as addition of numbers, or intersection
of sets etc.) is an object i so that, for all objects x, i x = x i = x. Find, identities for the
operations set union
MATH*2000 Fall 2012 Lab #1
Thursday, September 13
Note: For false statements/contradictions, it may be worthwhile to consider an example.
Problem 0.1. Using truth tables, show that the following distributive law holds for any three
statements p, q, r:
p (
Math 2000: Set Theory
Assignment 8
Due Date: Nov. 19 2012
Problem 1. For the following function, show that the function is injective and nd the functions range.
Then nd the inverse of that function (restrict the codomain of the function to be its range if