This preview shows page 1. Sign up to view the full content.
58
Solutions to Exercises
(b)
0
=
{x
E R
I
f{x)
=
f{O)
=
O}
= [0,1);
7/5
= [1,2)
since L7/5J
=
1;
3/4
= [1,0)
since
L
3/4J
=
1.
(c)
I
=
{I};
2
=
{2, 3, 6};
4
=
{4};
5
=
{5}.
28. (a) [BB] Here are the functions X
+
Y:
({a,
1),
{b,
In
({a,
1),
{b,
2n
({a,
1),
{b,
3n
({a,
2),
{b,
In
({a,
2),
{b,
2n
({a,
2),
{b,
3n
({a,
3),
{b,
In
({a,
3),
{b,
2n
({a,
3),
{b,
3n.
Here are the functions
Y
+
X:
{{I,a),{2,a),{3,a)}
{{I,a),{2,a),{3,b)}
({I,
a),
(2,
b),
{3,
an
({I,
a),
(2,
b),
{3, bn
({I,
b),
(2,
a),
{3,
an
({I,
b),
(2,
a),
{3, bn
({I,
b),
(2,
b),
{3,
an
({I,
b),
(2,
b),
{3, bn.
(b) [BB] There are no onetoone functions
Y
+ X. The onetoone functions from X +
Y
are
({a,
1),
{b,
2n
({a,
1),
{b,
3n
({a,
2),
{b,
In
({a,
2),
{b,
3n
({a,
3),
{b,
In
({a,
3),
{b,
2n.
(c) [BB] There are no onto functions X +
Y.
The onto functions
Y
+ X are
({I,
a),
(2,
a),
{3, bn
({I,
a),
(2,
b),
{3,
an
({I,
a),
(2,
b),
{3, bn
({I,
b),
(2,
a),
{3,
an
({I,
b),
(2,
a),
{3, b)J
({I,
b),
(2,
b),
{3,
an.
29. (a) There are no onetoone functions
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

Click to edit the document details