Write the following sets in set-builder (Rule Method) form:
$B_{1} = 6, 9, 12, 15, . . . . . . . . .$

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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 breifest possibel way to represent the elements of the set.

Given, $B_{1} = 6, 9, 12, 15, . . . . .$
As,
$6 = 3 \times 2$
$9 = 3 \times 3$
$12 = 3 \times 4$
$15 = 3 \times 5$
and so on.
So, we can see that the elements of $B_{1}$ are the multiples of 3 starting from second multiple $(6)$ .

Therefore, $B_{1}$ is ${x : x = 3 n; n \in N, n \geq 2}$

Hence, the set builder form of $B_{1}$ is
$B_{1} = {x : x = 3 n; n \in N, n \geq 2}$

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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_{1}

B_{4}

8, 27, 64, 125, 216

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

B_{6}

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