(Solved): Problem 8. ( 6 Points) Consider the set A={21,43,65,87,} Which one(s) among the foll ...

Problem 8. ( 6 Points) Consider the set $$A=\left\{\frac{1}{2},\frac{3}{4},\frac{5}{6},\frac{7}{8},\dots \right\}$$ Which one(s) among the following suggestions below describe(s) it correctly. (Simply answer by Yes or No -no justification required). 1. $$A=\{x?\mathbb{R}$$ : 'there exists $$m?\mathbb{N}$$ satisfying $$x=\frac{2m?1}{2m}\}$$ 2. $$A=\left\{\frac{2m?1}{2m}:m?\mathbb{N}\right\}$$ 3. $$A=\{x?\mathbb{R}:\frac{2m?1}{2m}$$ and $$m?\mathbb{N}\}$$ 4. $$A=\{x?\mathbb{Q}:\frac{2m?1}{2m}$$ and $$m?\mathbb{N}\}$$ 5. $$A=\{x?\mathbb{Q}$$ : there exists $$m?\mathbb{N}$$ satisfying $$x=\frac{2m?1}{2m}\}$$ 6. $$A=\{\frac{2m?1}{2m}:m?\mathbb{Z}$$ and $$m?1\}$$