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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 Spring '08
 [email protected]
 Equivalence relation, Transitive relation, relation

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