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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, …..}(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} |
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Answer» (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.
Here, {x : x = 1/n, n ∈ N} This is read as x is such that x = 1/n, here n ∈ N.
This is read as x is such that C is the set of multiples of 3 including 0.
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.
Since, {x : x = 0} This is read as x is such that E is an integer equal to 0.
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.
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} |
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