Question

The set builder form of $\{\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}\}$ is

• A. $\{x:x=\frac{n}{n+1}$, where $n$ is a natural number and $1\le n\le 6\}$
• B. $\{x:x=\frac{n}{n+1}$, where $n$ is a natural number and $1\le n\le 5\}$
• C. $\{x:x=\frac{n}{n+1}$, where $n$ is a natural number and $2\le n\le 6\}$
• D. $\{x:x=\frac{n}{n-1}$, where $n$ is a natural number and $1\le n\le 5\}$

Answer 1

The correct option is B $\{x:x=\frac{n}{n+1}$, where $n$ is a natural number and $1\le n\le 5\}$

Given, $\{\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6}\}$
Here every element is of the form $\frac{k}{k+1},$ where $1\le k\le 5$
$\therefore$ In set builder form, the set can be written as:
$\{x:x=\frac{n}{n+1};1\le n\le 5\text{and}n\in N\}$