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}
(i) {x:x ϵ N,x<7}
This is read as x is such that x belongs to natural number and x is less than 7. It satisfies all condition of roster form.
(ii) {x ϵ z: x=1/n+1,n ϵ W}
This is read as x is such that x is an integer greater than or equal to 0. And it’s value is 1/x+1.
(iii) {x N: x = 3n, n W}
(iv) {x:x ϵ N,9<x<16}
(v) {x:x=0}
(vi) {x ϵ N: x=n2,n≤10, n ϵ N}
(vii) {x N: x = 2n, n N}
(viii) {x N: x = 5n,0<n<6 N}