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Prof. Bjorn Poonen
October 16, 2001
MATH 55 MIDTERM (yellow)
Do not write your answers on this sheet.
Instead please write your name, your
student ID, your TA’s name, your section time, “yellow,” and all your answers in
your blue books. Total: 100 pts., 75 minutes.
(1)
(5 pts. each) For each of (a)(g) below: If the proposition is true, write TRUE.
If the proposition is false, write FALSE. (Please do not use the abbreviations T and
F, since in handwriting they are sometimes indistiguishable.) No explanations are
required in this problem.
(a) The set
{
0
,
1
}
*
of bit strings of ﬁnite length is a countable set.
(b) The proposition
∃
x
∀
y
(
x
≥
y
) is true, when the universe of discourse is the
set of natural numbers.
(c) The numbers 34
,
35
,
36 are pairwise relatively prime.
(d) There are inﬁnitely many integers
x
satisfying both
x
≡
12 (mod 99) and
x
≡
16 (mod 100). (Hint: you don’t need to solve this system.)
(e) The function 3
n
2
log
n
+ 5
n
(log
n
)
4
is
O
(
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This note was uploaded on 03/08/2010 for the course MATH 55 taught by Professor Strain during the Spring '08 term at University of California, Berkeley.
 Spring '08
 STRAIN
 Math

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