Solution to Let S be the set of bit strings of length no larger than 6, and … - Sikademy
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Archangel Macsika

Let S be the set of bit strings of length no larger than 6, and define an equivalence relation R on S as follows: (x, y) ϵ R if and only if x and y are of the same length. Specify the partition P of S that arises from R.

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Denote by |x| the length of a string x. Therefore, (x, y) \in R if and only if |x|=|y|. Then |x|\in\{1,2,3,4,5,6\} for each x\in S. The equivalence class [x] of a bit string x is defined as [x]=\{v\in S\ :\ (v,x)\in R\}=\{v\in S\ :\ |v|=|x|\}. Therefore, there are 6 equivalence classes. The partiton P=\{A_1,A_2,A_3,A_4,A_5,A_6\} consist of 6 sets. The set A_i contains all bit string of length i for i\in\{1,2,3,4,5,6\}.

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