2021HSCMultiple choice

Q5

1 mark

Question

Which of the following statements is FALSE?

A. $\forall a,b\in\mathbb R$ , $a<b\Rightarrow a^3<b^3$ .
B. $\forall a,b\in\mathbb R$ , $a<b\Rightarrow e^{-a}>e^{-b}$ .
C. $\forall a,b\in(0,+\infty)$ , $a<b\Rightarrow\ln a<\ln b$ .
D. $\forall a,b\in\mathbb R$ , with $a,b\ne0$ , $a<b\Rightarrow\frac1a>\frac1b$ .

Try the question before revealing the answer.

Syllabus alignment

Proof

The Nature of ProofUse formal proof language, contradiction, counter-examples and rigorous arguments involving numbers and inequalities.

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