TMUA Practice Question — Worked Solution

P2·Logic & Quantifiers·3.0CrackTMUA Original

proof-errorsquaring-inequalitysignflawed-step

Below is an attempted proof of the claim 'for every real

x

, if

x < 3

then

x^{2} < 9

'. At which line does the argument first break down?

Line 1

Suppose

x < 3

Line 2

Then

3 - x > 0

Line 3

Squaring both sides of

x < 3

gives

x^{2} < 9

Line 4

Therefore, for every real

x

with

x < 3

, we have

x^{2} < 9

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