Question

Write the set $\{\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6},\frac{6}{7}\}$ in the set-builder form.

Answer 1

Given: Set $\{\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{5}{6},\frac{6}{7}\}$

We know, each member in the given set has the numerator one less than the denominator.

Also, the numerator begins form $1$ and does not exceed $6$.

Hence, set builder form of the given set is

$\{x:x=\frac{n}{n+1},\text{where}n\epsilon N\text{and}1\le n\le 6\}$