Prof. Bjorn Poonen
October 16, 2001
MATH 55 MIDTERM (white)
Do not write your answers on this sheet.
Instead please write your name, your
student ID, your TA’s name, your section time, “white,” 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 value of (

141)
mod
8 is

5.
(b) The function 3
n
2
log
n
+ 5
n
(log
n
)
4
is
O
(
n
3
).
(c) The ceiling function
f
(
x
) =
d
x
e
, considered as a function from
R
to
R
, has
an inverse function.
(d) The set
{
1
,
2
,
3
} ×
Z
is countable.
(e) The proposition
∀
x
∃
y
(
x
≤
y
) is true, when the universe of discourse is the
set of natural numbers.
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 Spring '08
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 Math, Prime number, Inverse function, Injective function, Prof. Bjorn Poonen

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