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Recall that we have proven that we have the relation “ mod n” on the integers...

Recall that we have proven that we have the relation “ mod n” on the integers where a ≡ b mod n if n | b − a . We call the set of equivalence classes: Z/nZ. Show that addition and multiplication are well-defined on the equivalence classes by showing

(a) that you have a definition of addition and multiplication for pairs which matches your intuition and

(b) that if you choose different representatives when you add or multiply, the final result is invariant under this choice and

(c) define division for some pairs and show that this is well-defined as well.

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