BROCK
UNIVERSITY
Final
Examination:
December 2009
Course:
MATH
IP66
Date
of
examination: 15
December 2009
Time
of
examination: 09:00  12:00
Page 1 of 10
Number
of pages: 10
Number
of
students: 133
Number
of
hours: 3
hours
Instructor:
B.
Farzad
Examination Aids: One 8.5"
X
11" sheet of paper, handwritten on both sides. No other examination
aids are permitted. In particular, calculators are not permitted.
Student
Number:
Last (Family)
Name(s):
First (Given)
Name(s):
Do
not
turn this page until you have received the signal
to start.
(In
the
meantime, please
fill
out
the
identification section above,
and
read
the
instructions below
carefully.)
MARKING
GUIDE
This final examination consists of 7 questions on 10 pages (including
this one), printed on one side of the paper.
When you receive the signal
to start,
please
make
sure that your copy
of
the examination is complete
and
write your student number where indicated
at
the bottom
of
every
page
(except page 1).
Answer each question directly on the examination paper, in the
space provided, and use the reverse side of the pages for rough work.
If
you need more space for one of your solutions, use the reverse side of a
page and
indicate clearly the part
of
your work that should
be marked.
Good Luck!
Total Pages
=
10
Page 1
# 1:
# 2:
# 3:
#4:
# 5:
#6:
# 7:
TOTAL:
/10
/10
/10
/10
/10
/10
/10
/70
CONT'D .
..
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View Full DocumentDecember 2009
FINAL EXAMINATION
MATHIP66
Question
1.
[10 MARKS]
(1
point each) You do not need to justify your answer for the following questions.
(a) Make sure that you filled out the identification section write your student number where indicated
at the bottom of every page.
(b) What is
(k~1 ~
where
Ai
=
{i, i
+
1, i
+
2,
... }.
(c) Find the error in the following proof of this "theorem":
"Theorem: Every positive integer equals the next larger positive integer. "
"Proof: Let
P(n)
be the proposition
"n
=
n
+
1". To show that
P(k)
implies
P(k
+
1), assume that
P(k)
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 Spring '10
 JEFFHAROUTUNIAN
 Math, Logic, Mathematical Induction, Inductive Reasoning, Natural number

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