The answers to exercises marked IBB] can be found in the Back of the Book.[BB] For a, b ∈R...

The answers to exercises marked IBB] can be found in the Back of the Book.

[BB] For a, b ∈R, define a ~ b if and only if a − b ∈ Z.

(a) Prove that ~ defines an equivalence relation on Z.

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(b) What is the equivalence class of 5? What is the equivalence class of ?

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(c) What is the quotient set determined by this equivalence relation?