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Question

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}

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Solution

(i) {3,6,9,12}
={x:x=3n,nϵN and 1n4}
Alternatively, {x:x is a multiple of 3 and x12}
(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}={x:x=2n,nϵN and 1n5}
(iii) {5,25,125,625}
It can be seen that 5=51,25=52,125=53, and 625=54.
{5,25,125,625}={x:x=5n,nϵN and 1n4}
(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}
{1,4,9...100}={x:x=n2,nϵN and 1n10}
Alternatively, {x:x is a square of natural number and x100}

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