Write the following sets in set-builder (Rule Method) form:
$B_{4}$ ={ $8, 27, 64, 125, 216$ }

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Solution

Step: Express the given set in Set builder (Rule Method) form:

In set builder form, the actual elements of the set are not written, but a statement or a formula or a rule is written in briefest possible way to represent the elements of the set.
Given:
$B_{4}$ ={ $8, 27, 64, 125, 216$ }
As,
$8 =$ $(2)^{3}$
$27 =$ $(3)^{3}$
$64 =$ $(4)^{3}$
$125 =$ $(5)^{3}$
$216 =$ $(6)^{3}$

So, $B_{4} = 2^{3}, 3^{3}, 4^{3}, 5^{3}, 6^{3}$

Therefore, elements of $B_{4}$ are the cubes of natural number starting from 2 to 6.

Hence, set builder form of $B_{4}$ is
$B_{4} = {x : x = n^{3}; n \in N a n d 2 \leq n \leq 6} .$

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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} = 11, 13, 17, 19

B_{6} = {...., -6, -3, 0, 3, 6, ....}

B_{1} = 6, 9, 12, 15, . . . . . . . . .

B_{1}

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