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James Chen TMUA Paper 1 · Q12

Paper 1Logic & proof

Which line in this false proof that 1=21=2 contains the first mistake?

Let a=b(1)a2=ab(2)a2−b2=ab−b2(3)(a+b)(a−b)=b(a−b)(4)a+b=b(5)a+a=a(6)1=2(7)\begin{aligned} \text{Let }a&=b &&(1)\\ a^2&=ab &&(2)\\ a^2-b^2&=ab-b^2 &&(3)\\ (a+b)(a-b)&=b(a-b) &&(4)\\ a+b&=b &&(5)\\ a+a&=a &&(6)\\ 1&=2 &&(7) \end{aligned}
A(1)
B(2)
C(3)
D(4)
E(5)
F(6)
G(7)

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