TMUA Practice Question — Worked Solution

P2·Logic & Quantifiers·6.0CrackTMUA Original

proof-errordivision-by-zerolost-rootflawed-argument

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

x

, if

x^{2} = x

then

x = 1

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

Line 1

Suppose

x

is a real number with

x^{2} = x

Line 2

Then

x^{2} - x = 0

Line 3

Factorising gives

x (x - 1) = 0

Line 4

Dividing both sides by

x

gives

x - 1 = 0

Line 5

Therefore

x = 1

, as claimed.

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