Write each of the following sets in set-builder form :

(i) A = {4, 6, 8, 9, 10, 12, 14, 15, 16, 18}.

(ii) B = {1, 2, 3, 5, 6, 10, 15, 30}.

(iii) C = {-9, -6, -3, 0, 3, 6, 9, 12, 15}.

(iv) D = $\Big\lbrace\dfrac{1}{2},\dfrac{2}{3},\dfrac{3}{4},……………,\dfrac{8}{9}\Big\rbrace$.

(v) E = $\Big\lbrace\dfrac{1}{3},\dfrac{1}{5},\dfrac{1}{7},\dfrac{1}{11},\dfrac{1}{13},\dfrac{1}{17},\dfrac{1}{19}\Big\rbrace$.

(vi) F = {April, June, September, November}.

(vii) G = {0}.

(viii) H = { }.

(i) A = {4, 6, 8, 9, 10, 12, 14, 15, 16, 18}.

These are composite numbers (numbers with more than two factors) less than 20.

∴ A = {x : x is a composite number, 1 < x < 20}

(ii) B = {1, 2, 3, 5, 6, 10, 15, 30}.

These are all the natural numbers that divide 30 without a remainder.

∴ B = {x : x is a factor of 30}

(iii) C = {-9, -6, -3, 0, 3, 6, 9, 12, 15}.

These are multiples of 3 ranging from -9 to 15.

∴ C = {x : x = 3n, n ∈ I, -3 ≤ n ≤ 5}

(iv) D = $\Big\lbrace\dfrac{1}{2},\dfrac{2}{3},\dfrac{3}{4},……………,\dfrac{8}{9}\Big\rbrace$.

Each element is a fraction where the denominator is 1 more than the numerator $\Big(\dfrac{n}{n+1}\Big)$, and the numerator n is a natural number from 1 to 8.

∴ $D = {x : x = \dfrac{n}{n+1}, n \in N \text{ and } 1 \le n \le 8}$

(v) E = $\Big\lbrace\dfrac{1}{3},\dfrac{1}{5},\dfrac{1}{7},\dfrac{1}{11},\dfrac{1}{13},\dfrac{1}{17},\dfrac{1}{19}\Big\rbrace$.

The denominators are prime numbers between 2 and 20.

∴ $E = {x : x = \dfrac{1}{n}, n \text{ is prime, } 2 \lt n \lt 20}$

(vi) F = {April, June, September, November}.

These are the specific months of the year that contain exactly 30 days.

∴ F = {x : x is a month of the year having 30 days}

(vii) G = {0}.

Zero is the only whole number that is not a natural number.

∴ G = {x : x + 1 = 1, x ∈ W}

(viii) H = { }.

An empty set contains no elements. We can describe it using a property that is impossible to satisfy.

∴ H = {x : x is a number, x ≠ x}