(Solved): Let \( |x| \) denote the absolute value of \( x \). Give a counter-example to show that the follo ...

Let \( |x| \) denote the absolute value of \( x \). Give a counter-example to show that the following statement is false. \[ \forall x \in \mathbb{Q} \forall y \in \mathbb{Q} \forall z \in \mathbb{N}\left((x+y)^{z} \geq 5\right) \rightarrow(|x| \geq 2 \vee|y| \geq 2 \vee z \geq 2) \]