(i) A = {1, 2, 3, 4, 5, 6}
Since, {x : x ∈ N, x < 7}
This is read as x is such that x belongs to natural number and x is less than 7. It satisfied the all condition of roster form.
(ii) B = {1, 1/2, 1/3, 1/4, 1/5, …}
Here, {x : x = 1/n, n ∈ N}
This is read as x is such that x = 1/n, here n ∈ N.
(iii) C = {0, 3, 6, 9, 12, ….}
Since, {x : x = 3n, n ∈ Z+, is the set of positive integers}
This is read as x is such that C is the set of multiples of 3 including 0.
(iv) D = {10, 11, 12, 13, 14, 15}
Here, {x : x ∈ N, 9 < x < 16}
This is read as x is such that D is the set of natural numbers which are more than 9 but less than 16.
(v) E = {0}
Since, {x : x = 0}
This is read as x is such that E is an integer equal to 0.
(vi) {1, 4, 9, 16,…, 100}
Here,
12 = 1
22 = 4
32 = 9
42 = 16
.
.
.
102 = 100
Therefore, above set can be expressed in set-builder form as {x2: x ∈ N, 1≤ x ≤10}
(vii) {2, 4, 6, 8,….}
Here, {x: x = 2n, n ∈ N}
This is read as x is such that the given set are multiples of 2.
(viii) {5, 25, 125, 625}
Here,
51 = 5
52 = 25
53 = 125
54 = 625
Therefore, above set can be expressed in set-builder form as {5n: n ∈ N, 1≤ n ≤ 4}