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}

(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} = {*x*: *x* = 3*n*, *n*∈ N and 1 ≤ *n* ≤ 4}

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

It can be seen that 2 = 2^{1}, 4 = 2^{2}, 8 = 2^{3}, 16 = 2^{4}, and 32 = 2^{5}.

∴ {2, 4, 8, 16, 32} = {*x*: *x* = 2* ^{n}*,

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

It can be seen that 5 = 5^{1}, 25 = 5^{2}, 125 = 5^{3}, and 625 = 5^{4}.

∴ {5, 25, 125, 625} = {*x*: *x* = 5* ^{n}*,

**(iv)** {2, 4, 6 …}

It is a set of all even natural numbers.

∴ {2, 4, 6 …} = {*x*: *x* is an even natural number}

**(v)** {1, 4, 9 … 100}

It can be seen that 1 = 1^{2}, 4 = 2^{2}, 9 = 3^{2} …100 = 10^{2}.

∴ {1, 4, 9… 100} = {*x*: *x* = *n*^{2}, *n*∈N and 1 ≤ *n* ≤ 10}

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