I have come across a question in a Real Analysis assignment (contents of the question are not important), where I need to prove that:
(Statement 1 holds), if (Statement 2).
I'm confused about the terminology here. Do we need to show that
- if Statement 2 is true, then Statement 1 holds, OR
- Statement 1 is true only if Statement 2 holds?
Had the question been, if (Statement 2), (Statement holds), the former would work. However, the given terminology in the question has confused me.
You have to show : Statement 2 $\Rightarrow$ Statement 1.
Had they mentioned "Only if", you would have to show the opposite implication.