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Math 5615H.
October 5, 2011.
Midterm Exam.
Name (Print)
60 points are distributed between 5 problems.
You have 50 minutes (2:30 pm – 3:20 pm) to work on these problems.
No books, no notes. Calculators are permitted, however, for full credit,
you need to show stepbystep calculations.
This booklet consists of 7 page: the title page (this one), 5 pages (pp. 2–6)
contain 5 problems. The almost empty page 7 can also be used for solutions.
Some deﬁnitions:
The
union
of sets
{
E
α
, α
∈
A
}
[
α
∈
A
E
α
:=
{
x
:
∃
α
∈
A
such that
x
∈
E
α
}
.
The
intersection
of sets
{
E
α
, α
∈
A
}
\
α
∈
A
E
α
:=
{
x
:
∀
α
∈
A,
x
∈
E
α
}
.
The
complement
of
E
⊆
X
E
c
:=
{
x
∈
X
:
x /
∈
E
}
.
These operations satisfy the following properties:
1.
Distributivity:
A
∩
(
B
∪
C
) = (
A
∩
B
)
∪
(
A
∩
C
)
.
2.
DeMorgan’s Laws:
(
i
)
‡
[
α
∈
A
E
α
·
c
=
\
α
∈
A
E
c
α
,
(
ii
)
‡
\
α
∈
A
E
α
·
c
=
[
α
∈
A
E
c
α
.
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October 5, 2011.
Midterm Exam.
Page 2.
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This document was uploaded on 02/15/2012.
 Fall '09
 Math

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