Question

Describe the following sets in set-builder form:
(i) A = {1, 2, 3, 4, 5, 6};
(ii) $B=\left\{1,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.,...\right\};$
(iii) C = {0, 3, 6, 9, 12, ...};
(iv) D = {10, 11, 12, 13, 14, 15};
(v) E = {0};
(vi) {1, 4, 9, 16, ..., 100}
(vii) {2, 4, 6, 8 .....}
(viii) {5, 25, 125 625}

Answer 1

Set-builder form:
To describe a set, a variable x (each element of the set) is written inside braces. Then, after putting a colon, the common property P(x) possessed by each element of the set is written within braces.

$$\begin{gathered} \left(\mathrm{i}\right)\{x:x\in N,x<7\} \\ \left(\mathrm{ii}\right)\{x:x=\frac{1}{n},x\in N\} \\ \left(\mathrm{iii}\right)\{x:x=3n,n\in Z^{+}\} \\ \left(\mathrm{iv}\right)\{x:x\in N,9<x<16\} \\ \left(\mathrm{v}\right)\{x:x=0\} \\ \left(\mathrm{vi}\right)\{x^2:x\in N,1\le n\le 10\} \\ \left(\mathrm{vii}\right)\{x:x=2n,n\in N\} \\ \left(\mathrm{viii}\right)\{5^n:n\in N,1\le n\le 4\} \end{gathered}$$