NCERT Class XI Mathematics - Sets - Solutions

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Question : 4
Total: 73
Write the following sets in the set-builder form:
(i) {3, 6, 9, 12}
(ii) {2, 4, 8, 16, 32}
(iii) {5, 25, 125, 625}
(iv) {2, 4, 6, ...}
(v) {1, 4, 9, ..., 100}
Solution:  
(i) Let A = {3, 6, 9, 12}
All elements of the set are natural numbers that are multiples of 3.
∴ A = {x : x = 3n, n ∈ N and 1 ≤ n ≤ 4}
(ii) Let B = {2, 4, 8, 16, 32} = {21,22,23,24,25}
∴ B = {x : x = 2n, n ∈ N and 1 ≤ n ≤ 5}
(iii) Let C = {5, 25, 125, 625} = {51,52,53,54}
∴ C = {x : x = 5n, n ∈ N and 1 ≤ n ≤ 4}
(iv) Let D = {2, 4, 6, .......}
All elements of the set are even natural numbers.
∴ D = {x: x is an even natural number}
(v) Let E = {1, 4, 9, .........., 100}
All elements of the set are perfect squares.
∴ E = {x: x = n2, n ∈ N and 1 ≤ n ≤ 10}
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