The University of Sydney
MATH 1004
Second Semester
Discrete Mathematics
2011
Tutorial 3 Week 4
1.
Define
f
:
N
→
N
by
f
(
x
) =
x
+ 1. Determine whether or not
f
is
(a)
onetoone;
(b)
onto.
2.
Each of the following sets of pairs may or may not represent a function from
{
1
,
2
,
3
}
to
{
a, b, c, d
}
.
{
(1
,d
)
,
(2
,b
)
,
(3
,d
)
}
,
{
(1
,c
)
,
(2
,a
)
,
(3
,b
)
}
,
{
(1
,a
)
,
(3
,b
)
}
{
(1
,a
)
,
(1
,c
)
,
(3
,d
)
}
,
{
(2
,b
)
,
(3
,c
)
,
(1
,d
)
}
(
i
)
Identify the sets which represent functions and determine which of these
are onetoone.
(
ii
)
Explain clearly why each of the sets does or does not represent a function.
(
iii
) Explain clearly why each of the sets does or does not represent a oneto
one function.
3.
(
i
)
Let
A
=
{
1
,
2
,
3
,
5
,
7
,
11
}
and let
B
=
{
1
,
2
,...,
200
}
.
Is the function
f
:
A
→
B
given by
f
(
x
) =
x
2
onetoone?
(
ii
)
Now suppose that
A
=
{
2
,

1
,
2
,
3
,
5
,
7
,
11
}
and
B
=
{
1
,
2
,...,
200
}
. Is
the function
f
:
A
→
B
given by
f
(
x
) =
x
2
onetoone?
4.
Use arrow diagrams to write down all the functions from the set
{
1
,
2
}
to the
set
{
a,b,c
}
. How many are there? How many onetoone functions and how
many onto functions?
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 Three '11
 various
 Inverse function, 3 week, 1004 Second

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