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Clavis TMUA Set A Paper 2 · Q7

Paper 2Logic & proof

Here is an attempted proof of the following claim.

For all real numbers xx, if x3>xx^3>x then x>1x>1.

  • (I) Suppose x3>xx^3>x.
  • (II) Dividing both sides by xx gives x2>1x^2>1.
  • (III) Therefore x2−1>0x^2-1>0, so (x−1)(x+1)>0(x-1)(x+1)>0.
  • (IV) Hence x>1x>1 or x<−1x<-1.
  • (V) Therefore x>1x>1.

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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