MATH 239 Assignment 1
Spring 2007
This assignment is due at noon on Friday, May 11, 2007, in the drop boxes opposite the Tutorial
Centre, MC 4067.
1. A
onetoone correspondence
is a function
f
:
A
→
B
which is both onetoone and onto. If
a function
f
:
A
→
B
has the property that
x
=
y
⇒
f
(
x
) =
f
(
y
), then we say that
f
is
onetoone
. Function
f
is said to be
onto
if, for every
z
∈
B
, there is an
x
∈
A
such that
f
(
x
) =
z
. (Onetoone correspondences are an important enumerative technique, but we only
touch on them briefly in Section 1.1 of MATH 239.)
Determine whether or not each function defined below as onetoone, or onto, or both. Briefly
justify your answer.
(a) Let
f
:
Z
→
Z
be defined as
f
(
n
) =

2
n
2
+ 5.
(b) Let
g
:
Z
→
Z
be defined as
g
(
n
) = 5

2
n
.
(c) Let
B
=
{
b
1
b
2
. . . b
10
:
b
i
∈ {
0
,
1
} ∀
i,
1
≤
i
≤
10
}
be the set of all binary strings of length 10, and let
S
be all subsets of
{
1
,
2
, . . .
10
}
.
Define
h
:
B
→
S
to be
h
(
b
1
b
2
. . . b
10
) =
{
i
:
b
i
= 1
} ⊆ {
1
,
2
, . . . ,
10
}
.
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 Spring '09
 M.PEI
 Math, Natural number, binary strings

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