Science:Math Exam Resources/Courses/MATH220/December 2009/Question 06 (b)/Statement

Let $\mathbb{𝕀}$ be the set of irrational numbers. That is $\mathbb{𝕀}=\mathbb{ℝ}-\mathbb{\mathbb{Q}}$.

Decide whether the following statements are true or false. Prove your answers. Hint:The results from part (a) will be of great help.

(i) $\mathrm{\forall }x\in \mathbb{𝕀},\mathrm{\forall }y\in \mathbb{𝕀},xy\in \mathbb{𝕀}$.

(ii) $\mathrm{\forall }x\in \mathbb{𝕀},\mathrm{\exists }y\in \mathbb{𝕀}\text{s.t.}xy\in \mathbb{𝕀}$.