Question

The set-builder form of the set $\{\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32},\frac{1}{64}\}$ is

• A. $\{x:x=\frac{1}{2^n},\text{where}n\in W\text{and}n\le 6\}$
• B. $\{x:x=\frac{1}{2^n},\text{where}n\in N\text{and}n\le 6\}$
• C. $\{x:x=\frac{1}{2^n},\text{where}n\in N\text{and}n<6\}$
• D. $\{x:x=\frac{1}{2^n},\text{where}n\in W\text{and}n<6\}$

Answer 1

The correct option is B

$\{x:x=\frac{1}{2^n},\text{where}n\in N\text{and}n\le 6\}$

$\frac{1}{2}=\frac{1}{2^1}$

$\frac{1}{4}=\frac{1}{2^2}$

$\frac{1}{8}=\frac{1}{2^3}$

$\frac{1}{16}=\frac{1}{2^4}$

$\frac{1}{32}=\frac{1}{2^5}$

$\therefore$ The set builder form is

$\{x:x=\frac{1}{2^n},\text{where}n\in N\text{and}n\le 6\}$