Question

The set - builder form of the set $\{\frac{4}{5},\frac{5}{6},\frac{6}{7},\frac{7}{8},\frac{8}{9},\frac{9}{10}\}$ is

• A. $\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}4\le n\le 9\}$
• B. $\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}4<n<9\}$
• C. $\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}4\le n<9\}$
• D. $\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}4<n\le 9\}$

Answer 1

The correct option is A

$\{x:x=\frac{n}{n+1},\text{where}nϵN\text{and}4\le n\le 9\}$

$\frac{4}{5}=\frac{4}{4+1}$

$\frac{5}{6}=\frac{5}{5+1}$

$\frac{6}{7}=\frac{6}{6+1}$

$\frac{7}{8}=\frac{7}{7+1}$

$\frac{8}{9}=\frac{8}{8+1}$

$\frac{9}{10}=\frac{9}{9+1}$

$\Rightarrow$ If numerotor is n then the denominator is n+1

$\therefore$ The set builder form is

$\{x:x=\frac{n}{n+1},\text{where}\text{n}ϵ\text{N}\text{and}4\le n\le 9\}$