[Math] Why is this statement ‘There is a real number $x$ such that $x^2 < x$.' not true

discrete mathematicslogic

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)
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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)
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Best Answer

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 $x$."

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