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SOLVED: Let Z denote the set of all integers. And for the arbitrary positive integer n, define the equivalence relation Z" as (1.y) 1 mod n = y mod n. For the quotient set Z/Z", which is denoted as Z0, Z1, Z2, ..., Zn-1, where Zi = nk i | k ∈ Z for 0 < i < n - 1, answer the following:(a) Define the binary operation € on Z/Z" as: Zk € Zk' = Z(k k') mod n. For instance, for Z3, Z4 € Z/Z", Z2 € Z4 = Z(2 4) mod 3 = Z6 mod 3 = Z0.Prove that € is associative on Z/Z".(b) Prove that th
SOLVED: Let Z denote the set of all integers. And for the arbitrary posi…
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