CS 70
Discrete Mathematics for CS
Fall 2004
Rao
Midterm 1
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Three sides of 8.5 by 11 sheet of notes is permitted. No calculators are permitted. Do all your work on the
pages of this examination. If you need more space, you may use the reverse side of the page, but try to use
the reverse of the same page where the problem is stated.
You have 110 minutes. The questions are of varying difficulty, so avoid spending too long on any one
question.
Do not turn this page until the instructor tells you to do so.
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Total
CS 70, Fall 2004, Midterm 1
1
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View Full DocumentProblem 1. [True or false] (25 points)
Circle TRUE or FALSE. There is no need to justify your answers on this problem.
(a) TRUE or FALSE: If the implication
n
P
=
⇒
Q
is true, then
n
Q
=
⇒
P
.
True
(b) TRUE or FALSE: If
A
or
B
is true and
B
are true than
A
must be true.
(c) TRUE or FALSE:
gcd
(
n
+
1
,
2
n
+
1
) =
1
.
True.
Apply Euclid’s algorithm.
(d) TRUE or FALSE: For all
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 Spring '08
 PAPADIMITROU
 Graph Theory, Prime number, Eulerian path, Eulerian

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