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) `{2,4,5,….}`
(v) `{1,4,9,….,100}`.

Answer 1

(i) Elements of `{3,6,9,12}=3,6,9,12= 3n` where `1 le n le 4`
Therefore, `{3,6,9,12} = {x : x = 3n " where "1 le n le 4}`
(ii) Elements of `{2,4,8,16,32} = 2,4,8,16,32 = 2^(n)` where `1 le n le 5`
Therefore, `{2,4,8,16,32}={x : x = 2^(n) " where " 1 le n le 5}`
(iii) Elements of `{5,25,125,625} = 5,25,125,625 = 5^(n)"where" 1 le n le 4`
Therefore, `{5,25,125,625} = {x :x = 5^(n) "where" 1 le n le 4}`
(iv) Elements of `{2,4,6,....}=` collection of even
Therefore, `{2,4,6,.....} = {x : x " is an even natural number"}`
(v) Elements of `{1,4,9,....,100} = 1,4,9,....,100`
Therefore, `{1,4,9,...,100} = {x : x = n^(2) "where" 1 le n le 10}`.