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assignment8

# For example 2 3 1 5 4 means that 1 2 2 3 3

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Unformatted text preview: ppose µ is a permutation of S = {1, 2, 3, 4, 5}. This permutation can be defined as a set of 5 ordered pairs, but we introduced a shorter notation – an ordered list of elements of S: [µ(1) µ(2) µ(3) µ(4) µ(5)]. For example, µ = [2 3 1 5 4] means that µ(1) = 2, µ(2) = 3, µ(3) = 1, µ(4) = 5, µ(5) = 4. a) If µ = [2 3 1 5 4], what is the symbol (i) for µ2? (ii) For µ3? (iii) For (µ3)2? b) Let µ be as above and ν = [5 2 3 4 1]. (i) What is the symbol for µν? (ii) What is the symbol for νµ? c) Define the identity ι: S → S by ι(k) = k for all k in S. Is ι a permutation? If so, what is its symbol? d) If µ is as above, what is the symbol for µ ­1? Problem 8 4 The set Z5, the integers mod 5, can be represented by symbols {0, 1, 2, 3, 4}. For each element k of Z5, define the multiplication m...
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