HW7F07
CS336
Page 158160 READ
Page 162: 31,33,36,37
Read Chapter 5
Page 344: 4,11,15,31,33,41
Page 353: 1,3,19
Page 361: 5a,6a,10,11,21,27
(We only give solutions for evennumbered exercises and some selected odd
numbered exercises, because the answers to oddnumbered exercises are at the
back of the book.)
Page 162:
36. Show that a subset of a countable set is also countable.
Solution:
Let
A
be a countable set. We will show that any subset of
A
is also countable.
If the subset is finite, it is countable. If it is infinite, then that means that
A
is infinite. Since
A
is countably infinite, it is possible to list the elements of
A
in a sequence (indexed by the positive integers). We can make a new sequence
by taking the sequence for
A
and dropping the elements not in the subset, and
this proves that the subset is countably infinite.
Page 344:
4. 12
*
2
*
3 = 72.
11. Since there are two choices (0 and 1) for the eight positions other than
the beginning and ending positions, the number of such strings is 2
8
= 256.
15. 26
4
+ 26
3
+ 26
2
+ 26 + 1, where 26
4
,
26
3
,
26
2
,
26 stand for the number of
lowercase strings of length 4, 3, 2, and 1, respectively. The additional 1 accounts
for the empty string.
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 Spring '08
 Myers
 Natural number, Countable set, ABCDE

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