Proof Assignment 1
The following proof is due at the beginning of class on Monday, Sept. 21.
Problem 1: Let a, b, c Z. Prove that if a | b and a | c, then for any m, n Z
it is the case that a | mb + nc.
A Note Regarding the Write-Up of Proofs: When writin
Proof Assignment 2
The following proof is due at the beginning of class on Wednesday, Oct. 7.
Problem 1: Prove the following. (You should feel free to assume the reader
knows the quadratic formula from high school.)
Let a, b Z with a = 0. If a does not di
The following problems are due at the beginning of class on Wednesday,
Sept. 9. Please follow all guidelines as described in the Homework section of
the course syllabus. Also remember that homework can and should be worked
on and discussed wi
The following problems are due at the beginning of class on Wednesday, Oct. 7.
[1/n, n] = (0, ).
Problem 1: (2 points) Prove that
Problem 2: For n N let P (n) denote the proposition n2 + 5n + 1 is even.
(a) (1 point) Prove that if P (n) is
The following problems are due at the beginning of class on Wednesday, Oct. 21.
Problem 1: Consider the following relations on N.
R = cfw_(1, 5), (2, 3), (3, 2), (5, 2)
S = cfw_(2, 4), (3, 4), (3, 1), (5, 5).
(a) (1 point) Compute R S and
The following are due at the beginning of class on Wednesday, October 28.
Problem 1: (0.5 points) Let A = cfw_1, 2, 3, 4, 5, B = cfw_2, 3, C = cfw_1, 2, 3,
D = cfw_2, 3, 4, and E = cfw_2. Let the collection A = cfw_A, B, C, D, E be partially
Zermelo-Fraenkel Axioms for Sets
Undened terms: sets, membership (We shall think of the elements of sets
as being sets themselves.)
Axiom 1: (The axiom of extension) Two sets are equal if and only if they
have the same elements.
Axiom 2: (The axiom of the
What distinguishes some athletes is not so much their technical skilis as
their intuitive understanding of their sport. In baseball, they are the fielders
who always get a jump on the ball; in basketball, they are the players who
have "court sens