COT310001, Spring 2000
Assigned: 3/8/2000
Dutton and Lang
Assignment #4 (40 pts.)
Due: 3/22 in class
First, we
define
when two functions are considered equal (or identical). Two functions
f
:
A
→
B
and
g
:
A
→
B
are said
equal
, denoted
f
=
g
, if
f
(
x
) =
g
(
x
) for every
x
∈
A
, where
A
is the common
domain of the two functions.
For example, two functions
f
(
x
) = (
x
+ 1)
2
and
g
(
x
) =
x
2
+ 2
x
+ 1,
both defined from
R
to
R
, where
R
denotes the set of real numbers, are equal because (
x
+ 1)
2
=
x
2
+ 2
x
+ 1, by algebra laws.
1.
(10 pts.) Consider a set
A
= {1, 2}, a set
B
= {
a
,
b
,
c
}, and a set
C
= {
x
,
y
}.
Define a relation
R
⊂
A
×
B
as
R
= {(1,
a
), (1,
c
), (2,
b
)}, a relation
S
⊂
B
×
C
as
S
= {(
a
,
x
), (
b
,
y
), (
c
,
x
)},
and a relation
T
⊂
C
×
A
as
T
= {(
x
, 1), (
y
, 2)}.
Now answer each of the following questions
with a short explanation.
(a)
Is
R
a function?
If so, is it an injection?
(b)
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 Spring '09
 Set Theory, Inverse function, Surjection

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