Sets and Logic
MHF3202
SeLoC
Prof. JLF King
31Dec2009
C1:
Essay, on your own paper, triplespaced.
Please prove:
Thm
:
There are
∞
ly many prime numbers.
Start with. . .
Proof:
FTSOContradiction, suppose
p
1
<
p
2
<
· · ·
<
p
k
<
· · ·
<
p
L

1
<
p
L
*
:
is a list of
all
prime numbers. I will now produce a
prime
q
which
differs
from every member of (
*
), as
follows.
(
Continue your proof from here.
)
Short answer.
For
(C2)
and
(C3)
, show no work;
please fillin each blank on the problemsheet.
C2:
Please write
DNE
in a blank if
the described object does
not exist or if the indicated operation cannot be performed.
z
Prof.
King
believes
that
writing
in
com
plete, coherent sentences is crucial in communicating
Mathematics, improves posture, and whitens teeth.
Circle
one:
True!
Yes!
wH’at S a?sEnTENcE
a
Repeating decimal 0
.
1
14 equals
n
d
, where posints
n
⊥
d
are
n
=
. . . . . . . . . . . . . .
and
d
=
. . . . . . . . . . . . . .
.
b
Note that Gcd(15
,
21
,
35) = 1.
Find particular
integers
S, T, U
so that 15
S
+ 21
T
+ 35
U
= 1:
S
=
. . . . . . . . . .
,
T
=
. . . . . . . . . .
,
U
=
. . . . . . . . . .
.
[
Hint:
Gcd
`
Gcd(15
,
21)
,
35
´
= 1.
]
c
The number of ways of having 3 objects from 6
distinct types is
s
3
6
{
Binom
===
coeff
. . . . .
Single
====
integer
. . . . . .
.
And
q
3
6
y
=
q
K
L
y
, where
K
=
. . . . . . .
and
L
=
. . . . . . .
.
d
On
Z
+
, write
x
$
y
IFF Gcd(
x, y
)
>
2. So $ is
Transitive
T F
.
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 Fall '09
 LARSON
 ........., Prime number, Rational number, Divisor, Prof. JLF King

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