tmua.fyi Paper 2 Challenge 1 · Question 12

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tmua.fyi Paper 2 Challenge 1 · Q12

Paper 2Logic & proof

Consider this “proof” that $2=1$ . Let $a=b$ . Then $a^2=ab$ , so $a^2-b^2=ab-b^2$ , giving $(a+b)(a-b)=b(a-b)$ , hence $a+b=b$ ; with $a=b$ this gives $2b=b$ , so $2=1$ . The first invalid step is:

Awriting

a^2=ab

Bwriting

a^2-b^2=ab-b^2

Cfactorising both sides

Dcancelling the factor

(a-b)

Econcluding

2b=b

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