**True** or **False**

Positive real numbers $x$ and $y$ are such that $x+y < 2$. By AM-GM inequality, we have:

$\large xy+\frac{1}{xy}\ge2\sqrt{xy\left(\frac{1}{xy}\right)}=2$

Then is it true that $xy+\dfrac{1}{xy}$ has a minimum value of 2?

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