COT3100C01, Spring 2000
Assigned: 1/12/2000
S. Lang
Assignment #1 (40 pts.)
Due: 1/26 in class
Instructions:
Write your answer neatly and concisely.
All proofs need to be justified by
using the appropriate definitions, theorems, and logical reasoning.
Illegible scribbles or
unclear logic will result in minimum credit.
1.
(15 pts.) Recall the following definitions and a theorem:
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.
If the product of two integers is even, then at least one of them is even.
Use these definitions and the theorem (and other appropriate laws) to answer each of
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 Spring '09
 Logic, 6 pts, 2m, 12 pts, 7 pts

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