1.

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}

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.


(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}



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