COT 3100 Spring 2000
Exam #2
4/4/00
Lecturer: Arup Guha
TA: ________________
(Note: You will have 75 minutes for this exam. There are
100 points total to be earned. On some questions you can not
earn partial credit. Make sure to read AND follow all the
directions. If you need extra room for your work, put it on
the last page of the exam before the charts, and CLEARLY
number what problem’s work you are continuing.)
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1)
(1 pt each) True/False (Assume a, b, and c are positive integers for these questions.)
a) 0  a for all positive integers a.
True
False
b) The total number of prime numbers is infinite.
True
False
c) Euclid’s algorithm prime factorizes an integer.
True
False
d) All surjective functions are also bijections.
True
False
e) If f : A
→
B is a injection, then A < B.
True
False
f) If a  b and b  c then a  c, for all positive ints a,b and c
True
False
g) The Well Ordering Principle can be used to prove any
True
False
statement that can be proved by induction.
h) If a
≡
b (mod n) then n  (a
7
– b
7
+ 13n)
True
False
i) a
2
≡
0 (mod 4) or a
2
≡
1 (mod 4)
True
False
j) If f(x)=xa and g(x)=xb, then f(g(x)) = g(f(x))
True
False
2)
(2 pts each) Short Answer
a)
The Fundamental Theorem of Arithmetic states that
all positive integers can be
uniquely prime factorized.
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 Spring '09
 pts, Natural number, Prime number, base case, positive integers

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