Why is this statement 'There is a real number $x$ such that $x^2 < x$.' not true?

Determine whether the statements are true or false.
There is a real number $x$ such that $x^2 < x$.

My obvious answer was the statement is true,
take e.g. $x=0.5$

But the solution says otherwise: (Discrete Mathematics with Applications)

This is strange, is the answer wrong because all I need to show is that there exists one real number for this given statement to be true.

edit: added question screenshot: part b)

• If the question is what you say it is, then it seems like there's an error on the part of the author. Commented Nov 5, 2016 at 0:15
• I suspect that there's something wonky going on with the quantifiers here. As the question stands, yes, clearly there is such a number $x$, but it looks like the solution manual somehow interpreted it as meaning "for all values $x$". Commented Nov 5, 2016 at 0:15
• Looks strange to me. Perhaps there's a subtle distinction I don't see between "the truth value of the statement is true" and "the statement is false". Commented Nov 5, 2016 at 0:16
• @EthanBolker There really better not be . . . Commented Nov 5, 2016 at 0:17
• @Arthur It's not "controversial" so much as "wrong." :P Commented Nov 5, 2016 at 0:19

If this is correctly quoted, it is terribly incorrect. It looks like a copy/paste error: the text $$\mbox{The truth value of this statement is 'True' . . . but the statement is False}$$ makes me suspect that in an earlier draft, this was two examples - one of the form "there exists an $x$" and one of the form "for all $x$."