Define a relation ~ on Z x Z such that (a,b) ~ (c,d) precisely
when a...
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Define a relation ~ on Z x Z such that (a,b) ~ (c,d) preciselywhen a + b = c + d.
Let R = {[(a,b)] : (a,b) in Z x Z} (i.e. R is the set of allequivalence classes of Z x Z under the equivalence relation ~). Foreach of the following operations, determine whether or not theoperation 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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