Let B be the set of strings over alphabet {0,1}. Consider the following problem: Input: A string x from B Yes/No Question: Is x, when interpreted as a binary number, a multiple of 2?   Note that we ignore leading zeros when interpret the strings.  For example, we consider a string like ' 001 ' as the binary number 1. For /\, the empty string, we consider it as 0.   a. Give the three shortest yes input instances for this problem. b. Give the three shortest no input instances for this problem. c. Suppose that we list the strings in B in numerical order and break the ties based on the length of the strings. Which of the following strings have a fixed position on the list?   /\, 00, 1, 001, 10, 0000   d. From c), we have observed that when we list the strings in numerical order, some strings do not appear in a fixed position on the list. Does this prove that B is uncountably infinite? Why or why not?

Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
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  • Let B be the set of strings over alphabet {0,1}. Consider the following problem:

Input: A string x from B

Yes/No Question: Is x, when interpreted as a binary number, a multiple of 2?

 

Note that we ignore leading zeros when interpret the strings.  For example, we consider a string like ' 001 ' as the binary number 1. For /\, the empty string, we consider it as 0.

 

a. Give the three shortest yes input instances for this problem.

b. Give the three shortest no input instances for this problem.

c. Suppose that we list the strings in B in numerical order and break the ties based on the length of the strings. Which of the following strings have a fixed position on the list?

 

/\, 00, 1, 001, 10, 0000

 

d. From c), we have observed that when we list the strings in numerical order, some strings do not appear in a fixed position on the list. Does this prove that B is uncountably infinite? Why or why not?

 

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