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Daniel J Smith Custom TMUA Set A Paper 2 · Q17

Paper 2Algebra

Consider the claim:

For all integers aa, bb, cc, if ab=acab=ac then b=cb=c

A student's argument is as follows:

  • I. Suppose ab=acab=ac
  • II. Then ab−ac=0ab-ac=0
  • III. So a(b−c)=0a(b-c)=0
  • IV. Therefore b−c=0b-c=0
  • V. Hence b=cb=c

Which of the following best describes this argument?

AThe argument is completely correct.
BThe argument is incorrect, and the first error is on line I
CThe argument is incorrect, and the first error is on line II
DThe argument is incorrect, and the first error is on line III
EThe argument is incorrect, and the first error is on line IV
FThe argument is incorrect, and the first error is on line V

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