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# hw11 - CS 173 Discrete Structures Fall 2010 Homework 11...

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CS 173: Discrete Structures, Fall 2010 Homework 11 This homework contains 6 problems worth a total of 44 points. It is due on Friday, December 3rd at 4:00 pm. Put your homework in the appropriate dropbox in the Siebel basement. 1. Equivalence relations [10 points] The automatic quiz grading software at Hypothetical Middle School has problems with the fact that students often type a capital letter O for zero, or a small L for one. To grade their answers, we need to treat zero (let’s write it Z) as equivalent to O, and small L (let’s write it as L) as equivalent to 1. So, if k is any positive integer, suppose that A k is the set of strings of length between 1 and k , composed of the four characters 0, 1, Z, and L. Let R be the equivalence relation on A k in which two strings x and y are related (i.e. xRy ) if they represent the same binary number. That is, x and y have the same length and, at each corresponding string position, either (a) x and y both contain 0 or Z or (b) x and y both contain l or L. For example, the strings “00Z” and “000”, as are the strings

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hw11 - CS 173 Discrete Structures Fall 2010 Homework 11...

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