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. S
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
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 =
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.
Proo
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
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.
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 goo
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)
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 =
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 distr
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 (r