Question

Write the following sets in the set builder form.
(i) F = {5, 10, 15, 20}
(ii) G = { 9, 16, 25, 36, ..., 81}
(iii) H = {5¹, 5², 5³, 5⁴}
(iv) X = {8, $-$8}
(v) Y = $\left\{1,\frac{1}{8},\frac{1}{27},\frac{1}{64},\frac{1}{125}\right\}$

Answer 1

Set builder form: In this method, a set is described by a characterising property P(x) of its elements x. In such a case, the set is described as {x: P(x) holds}.

$\left(\mathrm{i}\right)\mathrm{F}=\left\{x\right|x=5n,n\in N,n\le 4\}$

$\left(\mathrm{ii}\right)\mathrm{G}=\left\{x\right|x=n^2,n\in N,3\le n<10\}$

$\left(\mathrm{iii}\right)\mathrm{H}=\left\{x|x=5^n,n\in N,n\le 4\right\}$

$\left(\mathrm{iv}\right)\mathrm{X}=\left\{x|\mathrm{square}\mathrm{of}x\mathrm{is}64\right\}$

$\left(\mathrm{v}\right)\mathrm{Y}=\left\{x|x=\frac{1}{n^3},n\in N,n\le 5\right\}$