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Question 4

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 upto infinity}
(v) {1, 4, 9, upto 100}

Answer

 (i) {3, 6, 9, 12} = {xx = 3nn∈ N and 1 ≤ n ≤ 4}

 

(ii) {2, 4, 8, 16, 32}

It can be seen that 2 = 21, 4 = 22, 8 = 23, 16 = 24, and 32 = 25.

∴ {2, 4, 8, 16, 32} = {xx = 2nn∈ N and 1 ≤ n ≤ 5}

 

(iii) {5, 25, 125, 625}

It can be seen that 5 = 51, 25 = 52, 125 = 53, and 625 = 54.

∴ {5, 25, 125, 625} = {xx = 5nn∈N and 1 ≤ n ≤ 4}

 

(iv) {2, 4, 6 …}

It is a set of all even natural numbers.

∴ {2, 4, 6 …} = {xx is an even natural number}

 

(v) {1, 4, 9 … 100}

It can be seen that 1 = 12, 4 = 22, 9 = 32 …100 = 102.

∴ {1, 4, 9… 100} = {xx = n2n∈N and 1 ≤ n ≤ 10}

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