Describe the following sets in Set-Builder form:(i) {0}(ii) {0, ±1, �

1.	Describe the following sets in Set-Builder form:(i) {0}(ii) {0, ±1, ±2, ±3}(iii) {1/2, 2/5, 3/10, 4/17, 5/26, 6/37, 7/50}(iv) {0, -1, 2, -3, 4, -5, 6,…}
Answer» (i) Let A = {0} 0 is a whole number but it is not a natural number. ∴ A = {x / x ∈ W, x ∉ N} (ii) Let B = {0, ±1, ±2, ±3} B is the set of elements which belongs to Z from -3 to 3. ∴ B = {x /x ∈ Z, -3 ≤ x ≤ 3} (iii) Let C = {1/2, 2/5, 3/10, 4/17, 5/26, 6/37, 7/50} ∴ C = {x/x = \(\frac{n}{n^2+1}\), n ∈ N, n ≤ 7} (iv) Let D = {0, -1, 2, -3, 4, -5, 6, …} ∴ D = {x/x = (-1)n-1 × (n – 1), n ∈ N}

Describe the following sets in Set-Builder form:(i) {0}(ii) {0, ±1, ±2, ±3}(iii) {1/2, 2/5, 3/10, 4/17, 5/26, 6/37, 7/50}(iv) {0, -1, 2, -3, 4, -5, 6,…}

Answer»

(i) Let A = {0}

0 is a whole number but it is not a natural number.

∴ A = {x / x ∈ W, x ∉ N}

(ii) Let B = {0, ±1, ±2, ±3}

B is the set of elements which belongs to Z from -3 to 3.

∴ B = {x /x ∈ Z, -3 ≤ x ≤ 3}

(iii) Let C = {1/2, 2/5, 3/10, 4/17, 5/26, 6/37, 7/50}

∴ C = {x/x = \(\frac{n}{n^2+1}\), n ∈ N, n ≤ 7}

(iv) Let D = {0, -1, 2, -3, 4, -5, 6, …}

∴ D = {x/x = (-1)n-1 × (n – 1), n ∈ N}