Question

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

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

Given the set $A=\{\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32},\frac{1}{64}\}$
$=\{\frac{1}{2^1},\frac{1}{2^2},\frac{1}{2^3},\frac{1}{2^4},\frac{1}{2^5},\frac{1}{2^6}\}.$
We can see that the denominators of the fractions in the set can be represented by $2^n,$ where $n\in N\text{and}n\le 6.$
So,the set builder form of A is
$\{x:x=\frac{1}{2^n},\text{where}n\in N\text{and}n\le 6\}$