Describe the following sets in set-builder form: (i) A = {1,2,3,4,5,6

1.	Describe the following sets in set-builder form: (i) A = {1,2,3,4,5,6} (ii) B = {1, \(\frac{1}2\) , \(\frac{1}3\), \(\frac{1}4\), \(\frac{1}5\),…..} (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}
Answer» (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)

Describe the following sets in set-builder form: (i) A = {1,2,3,4,5,6} (ii) B = {1, \(\frac{1}2\) , \(\frac{1}3\), \(\frac{1}4\), \(\frac{1}5\),…..} (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}

Answer»

(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)