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COT3100C01, Fall 2002
Assigned: 8/27/2002
S. Lang
Assignment #1 (40 pts.)
Due: 9/5 in class by 8:45 am
Instructions:
Write your answer neatly and concisely.
All proofs need to be justified step by step
by using the appropriate definitions, theorems, and logical reasoning.
Illegible scribbles or
unclear logic will result in minimum credit
.
1.
(16 pts.) Recall the following definitions and theorems about integers:
Definition
. An integer
a
is even if
a
= 2
b
for some integer
b
.
(That is, there exists an integer
b
such
that
a
= 2
b
.)
Definition
. An integer
a
is odd if
a
= 2
b
+ 1 for some integer
b
.
(That is, there exists an integer
b
such that
a
= 2
b
+ 1.)
Definition
. An integer
a
is a divisor of integer
b
, denoted
a

b
, if
a
≠
0 and there exists integer
c
such that
b
=
ac
.
Theorem.
Each integer is either even or odd (but not both).
Theorem.
The sum of two odd integers is even.
Theorem.
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