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}
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) $\left\{5^{n}: n \in N, 1 \leq n \leq 4\right\}$
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