Proof Writing · Medium problem

There is no positive real $x$ such that $x + \dfrac{1}{x} < 2$.

There is a positive real $x$ such that $x + \dfrac{1}{x} < 2$.

There is a positive real $x$ such that $x + \dfrac{1}{x} \ge 2$.

For every positive real $x$, $x + \dfrac{1}{x} < 2$.