Fill in the blanks in the following proof that the square of any rational number is rational:
Proof: Suppose that r is (a). By definition of rational, r = a/b for some (b) with b ≠ 0. By substitution,
r2 = (c) = a2/b2
Since a and b are both integers, so are the products a2 and (d) Also b2 = 0 by the (e) Hence r2 is a ratio of two integers with a nonzero denominator, and so (f) by definition of rational.
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