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UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
ECE190F — Discrete Mathematics
Final Examination
December 6, 2004
Examiners: John Carter, Ben Liang
Duration: 2.5 hours
•
This is a “closed book” examination; no aids are permitted.
•
No electronic or mechanical computing devices are permitted.
•
Write your answers in the spaces provided.
•
If necessary, use the backs of the pages for rough work.
•
Show all steps and present all results clearly. State any assumptions that you may make.
•
For full credit, answers to counting problems must be expressed as integers.
•
Please write clearly; if we cannot read an answer, we cannot mark it.
•
This examination has 11 pages (including this one). Be sure that you have a complete paper.
Name
Student Number
MARKS
Question
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Total
Value
6
3
6
4
5
4
6
6
4
4
5
7
4
14
6
6
6
4
100
Mark
Enter the frst letter oF
your Family name here.
1
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View Full Document 1. (6 marks)
Let
A
=
{
1
,
2
,
3
,
4
,
5
}
,
B
=
{
3
,
6
}
, and let
E
be the set of even integers. Find
(a)
A
∪
B
(b)
A

E
(c)
A
∩
E
(d)
P
(
B
)
(e)
B
× {∅}
(f) (
B
⊆
A
)
∨
(
B
⊆
E
)
2. (3 marks)
Let
p
and
q
be statements. Use a truth table to show that (
p
→
q
)
↔
(
∼
q
→∼
p
)i
sa
tautology.
3. (6 marks)
Let
F
(
x
) mean that student
x
is a frosh, and let
C
(
x, y
) mean that student
x
is enrolled in
class
y
, where the domain of
x
is the set of all students at U of T and the domain of
y
is the
set of all classes at U of T.
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This note was uploaded on 04/19/2008 for the course ECE 190 taught by Professor Carter during the Fall '06 term at University of Toronto Toronto.
 Fall '06
 Carter

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