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Clavis TMUA Set C Paper 2 · Q7

Paper 2Logic & proof

Here is an attempted proof of the following claim.

If aa and bb are real numbers with a2=b2a^2=b^2, then a=ba=b.

  • (I) Suppose a2=b2a^2=b^2.
  • (II) Then a2−b2=0a^2-b^2=0.
  • (III) Factorising gives (a−b)2=0(a-b)^2=0.
  • (IV) Hence a−b=0a-b=0.
  • (V) Therefore a=ba=b.

Which of the following is the case?

AThe proof is correct.
BThe proof is incorrect, and the first error occurs in line (I).
CThe proof is incorrect, and the first error occurs in line (II).
DThe proof is incorrect, and the first error occurs in line (III).
EThe proof is incorrect, and the first error occurs in line (IV).
FThe proof is incorrect, and the first error occurs in line (V).

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