I'm having trouble understanding how to prove this problem. I need some help.
Let a ∈ ℚ, a ≠ 0 and b ∈ ℝ \ ℚ. Prove the following:
a) a + b ∈ ℝ \ ℚ
b) ab ∈ ℝ \ ℚ
c)1/b ∈ ℝ \ ℚ
Thanks for any help provided
All you have to know is that the rational numbers $\displaystyle \mathbb{Q}$ is a field: closed under sum, multiplication and inverses (for elements different from zero, of course).