Write the following sets in set-builder (Rule Method) form :
$B_{3}$ = { $\frac{1}{3}, \frac{3}{5}, \frac{5}{7}, \frac{9}{11}, . . . . . . . . .$ }

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Solution

Since, the set has fractional elements with the numerators as odd numbers and the denominator as 2 more than the numerator, we have
We have $B_{3} =$ { $x : x = \frac{n}{n + 2},$ where n is an odd natural number }

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Similar questions

Write the following sets in roster set-builder (Rule Method) form:

(i) $B_{1} = {6, 9, 12, 15, . . . . . . . . .}$

(ii) $B_{2} = {11, 13, 17, 19.........}$

(iii) $B_{3} = {\frac{1}{3}, \frac{3}{5}, \frac{5}{7}, \frac{7}{9}, \frac{9}{11} . . . . . . . . .}$

(iv) $B_{4} = {8, 27, 64, 125, 216.........}$

(v) $B_{5} = {- 5, - 4, - 3, - 2, - 1.........}$

(vi) $B_{6} = {. . . . . . . . . . . - 6, - 3, 0, 3, 6.........}$

B_{2}

{\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7}}

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

B_{5}

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