Define a relation ~ on Z x Z such that (a,b) ~ (c,d) precisely when a...

Define a relation ~ on Z x Z such that (a,b) ~ (c,d) precisely when a + b = c + d.

Let R = {[(a,b)] : (a,b) in Z x Z} (i.e. R is the set of all equivalence classes of Z x Z under the equivalence relation ~). For each of the following operations, determine whether or not the operation is well defined. Prove your answer.

[(x,y)] * [(w, z)] = [(x + w, y + z)]

[(x,y)] * [(w, z)] = [(x² + w², y² + z²)]

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Expert Solution

Colby Messinger answered 10 months ago

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