SSCE HSC Mathematics Extension 2 The language of proof: Consider the following statement

Question

Consider the following statement about real numbers. ‘Whichever positive number $r$ you pick, it is possible to find a number $x$ greater than 1 such that $rac{ln x}{x^3} < r.$’ When this statement is written in the formal language of proof, which of the following is obtained? A. $\forall x > 1 \exists r > 0 \frac{ln x}{x^3} < r$ B. $\exists r > 1 \forall x > 0 \frac{ln x}{x^3} < r$ C. $\forall r > 0 \exists x > 1 \frac{ln x}{x^3} < r$ D. $\exists r > 0 \forall x > 1 \frac{ln x}{x^3} < r$

Consider the following statement about real numbers - HSC - SSCE Mathematics Extension 2 - Question 4 - 2023 - Paper 1

Worked Solution & Example Answer:Consider the following statement about real numbers - HSC - SSCE Mathematics Extension 2 - Question 4 - 2023 - Paper 1

Which of the following is obtained?

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