# Describe the following sets in set-builder form:

Question:

Describe the following sets in set-builder form:

(i) A = {1, 2, 3, 4, 5, 6};

(ii) $B=\{1,1 / 2,1 / 3,1 / 4,1 / 5, \ldots\}$;

(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}

Solution:

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.

(i) $\{x: x \in N, x<7\}$

(ii) $\left\{x: x=\frac{1}{n}, x \in N\right\}$

(iii) $\left\{x: x=3 n, n \in Z^{+}\right\}$

(iv) $\{x: x \in N, 9 (v)$\{x: x=0\}$(vi)$\left\{x^{2}: x \in N, 1 \leq n \leq 10\right\}$(vii)$\{x: x=2 n, n \in N\}$(viii)$\left\{5^{n}: n \in N, 1 \leq n \leq 4\right\}\$