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Section 2.1
31
(i) True. {{I, 2}} contains just one element, {I, 2}, and this is an element of {I, 2, {I, 2}}.
8. [BB] Yes it is; for example, let
x
=
{I} and
A
=
{I, {I}}.
9. (a) i.
{a, b,
e,
d}
ii. [BB]
{a, b,
e},
{a, b, d}, {a,
e,
d}, {b,
e,
d}
iii.
{a,b}, {a,e}, {a,d}, {b,e}, {b,d}, {e,d}
iv.
{a}, {b}, {e}, {d}
v.0
(b) 16
10. (a)
If
A
=
0, then
P(A)
=
{0} is a set containing one element, so
its
power set contains two elements.
(b)
P(A)
contains two elements;
P(P(A))
has four elements.
11.
(a)
[BB] 4;
(b)
[BB] 8.
(c) [BB] There are
2
n
subsets of a set of
n
elements. (See Exercise 15 in Section 5.1 for a proof.)
12. (a) [BB] False. Let
A
=
{2},
B
=
{{2}l,
C
=
{{
{2}}}. Then
A
is an element of
B
(that is,
A
E
B)
and
B
is an element of
C (B
E
C),
but
A
is not an element of
C
(since
B
is
C's
only element).
(b) True.
If
x
E
A,
then
x
E
B
since
A
~
B.
But since
x
E
B,
then
x
E
C
since
B
~
C.
(c) True. As in the previous part, we know that
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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

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