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SolHW7f07

# SolHW7f07 - HW7F07 CS336 Page 158-160 READ Page 162...

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HW7F07 CS336 Page 158-160 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 even-numbered exercises and some selected odd- numbered exercises, because the answers to odd-numbered 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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