Math 310, Homework 5, due 8th October 2012
You must justify all your answers, by giving a proof of your answer. You may use
any property of numbers you have studied.
(1) Assume we dene R R as below. Decide whether it is the graph of a
function from R to R

Math 310, Homework 6, due 15th October 2012
You must justify all your answers, by giving a proof of your answer. You may use
any property of numbers you have studied.
(1) We saw in class that if f : A B, g : B C are functions and g f is
injective, so is f

Homework 4, Math 310, due October 1st, 2012
Below are some exercises in writing proofs. Write them in English. In
particular, do not use the symbols , , . You may use other symbols
as you see t, but try not to overdo them, since it will make it harder
to

(1)
(2)
(3)
(4)
Homework 1, Math 310, due September 10
Decide whether the following sentences are mathematical statements or not.
(a) Where are my car keys?
(b) The earthworm soup is cold and the cactus milkshake is
warm.
(c) Keep your elbows o the table!

Midterm 2, Math 310, November 2nd, 2012
Read questions carefully. Please write legibly.
(1) (a) Given a relation on a set A, state the three conditions
which make it an equivalence relation.
(b) Let A = cfw_a, b, c, d be a set with four distinct elements.

Homework 2, Math 310, due September 17
(1) Writing truth tables, decide whether the two statements are
equivalent or not. A, B, C will denote some mathematical statements.
(a) A (B C) and (A B) (A C).
(b) A and A.
(c) A B and A B.
(d) A B and A B.
(2) If

Midterm 1, Math 310, 28, September, 2012, 10.10-11am
Please read questions carefully. Please write legibly.
(1) Decide which of the following are mathematical statements. I
expect only yes or no as answers. Be aware that English language is open to some i

Math 310, Homework 3, due 24th September 2012
(1) Write each of the following statement in English that does not
use quantier symbols. Write the negation of each of these in
symbolic form without using the negation symbol .
(a) (x Q)(x > 2).
(b) (x Q)(x2

Homework 7, Math 310, due October 22nd, 2012
(1) Dene a relation on R as follows. For a, b R, a b if ab Z.
Prove that this is an equivalence relation. Can you identify the
set of equivalence classes with the unit circle in a natural way?
(Hint: Trigonomet

Homework 8, Math 310, due October 29th, 2012
(1) Prove properties 3,4 and 5 on page 8 of the notes. Remember
that you are only allowed to use properties which are proved
before (including 1 and 2).
(2) The following are applications of the universal prope