(b) Define an operation on our construction of the integers by [(a, b) [(c, d)) = [(ad, be)] for all equivalence classes [(a, b)), [(c, d), where a, b, c, d e N. Is this operation well defined? Justify your answer.

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A:

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.