MATH 300-FINAL EXAM 1-12/8/2011.
Instructions. Six problems. Closed books, closed notes. Calculators and phones not allowed. No credit for answers without justication
complete proofs required. Time given: 120 minutes.
1. Let A, B, C be sets. Prove that A
MATH 300-PRACTICE TEST 2-Fall 2012
1. Let X be a non-empty set. Recall cfw_0, 1X deotes the set of all
functions f : X cfw_0, 1. Given a subset A X , the characteristic function
of A, fA : X cfw_0, 1 is dened by:
fA (x) = 1, x A;
fA (x) = 0, x A.
(i) Show
Math 300, Fall 2012/ Exam 1: 10/9/2012. Justify all answers for credit.
Time given: 75 minutes. Closed book, closed notes, no calculators.
1.[12] Write down the following statement symbolically (using quantiers), then write down its negation (symbolically
MATH 300-TEST 2-11/20/2012
1. [20]Recall that cfw_0, 1R denotes the set of all functions f : R cfw_0, 1.
Prove that the function:
: cfw_0, 1R P (R),
(f ) = cfw_x R|f (x) = 0
is injective.
2.[16] Find the multiplicative inverse of each nonzero element in
A
I
f-r I
'-l
o
(D
6'
0c
o
o
E
I
Ed's
I
+
\t
I
,
I
I
<D
o
s
oa
o
o
E'
oa
.<
t-
Htr
b.J
t-l
x
'ct
(D
ftJ
^?'t9
.^
l :-
# ls.
tiE
.) tat
EIE
J
g
6
6
vt
z
*
e
o
p
xu)
So.
; -.
T liiE
o\
l!1
;E'
9R
o
c)
(D
J
(D
o
cfw_
cfw_
I
E
<
lnt
qK.
" FF
Y
^
J
t
i
16
il t
Math 300: Intro to Abstract Math
Instructor:
Oce:
Phone:
e-mail:
Oce Hours:
Course Web Page:
Course Text:
Lectures:
Midterms:
Final:
Grade:
Grading Scheme:
Spring 2014
Dr. Heather Finotti
233 Ayres Hall
865.974.4320
heather@math.utk.edu (this is my prefer
Math 300, Fall 2012/ Practice Test (for Exam 1)
1. Write down (symbolically) the negation of the statement:
(x)x = 2 (y )(x + 2y xy ).
Which one is true: the statement or its negation? (The universe is R).
2. Prove that, for any sets S, T, U :
S \ (T U )
MATH 300-EXAM 2-11/10/2011. Instructions. Five problems. Closed
books, closed notes. No credit for answers without justicationcomplete
proofs required. Time given: 75 minutes.
1. Let R1 and R2 be partial orders on a set A. Show that R1 R2 is
also a partia
MATH 300-FINAL EXAM- 12/11/2012
Instructions. Closed books, closed notes. No credit for answers without justication. Time given: 120 min . EIGHT QUESTIONS.
1. [13] Write down (symbolically) the negation of the statement:
(x)x = 2 (y )(x + 2y = xy ).
Which
MIDTERM SURVEY: Math 300, Fall 2012
Instructions. The goal of this form is to gather student input to inform
the teaching of the second part of the course. Your comments will be read
only by me (Alex Freire) and can be made anonymously. Answering these
qu