Write the following sets in set builder (Rule Method) form:
$B_{6} = {...., -6, -3, 0, 3, 6, ....}$

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

As, $- 6, - 3, 0, 3, 6$ are the negative and positive multiples of 3.

Therefore, elements of $B_{6}$ are in the form of $3 n$ , where
$n \in Z .$

Hence, set builder form of $B_{6}$ is

$B_{6} = {x : x = 3 n, n \in Z} .$

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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_{6}

B_{2} = 11, 13, 17, 19

B_{4}

8, 27, 64, 125, 216

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

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