Describe the following sets in set-builder form:

**(i)** A = {1, 2, 3, 4, 5, 6}

**(ii) **\( B = {1, \dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}, \dfrac{1}{5}, …..}\)

**(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}

Asked by Sakshi | 1 year ago | 68

**(i)** A = {1, 2, 3, 4, 5, 6}

{x : x ∈ 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) **B =\( \{1, \dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}, \dfrac{1}{5}, …\}\)

{x : x = \( \dfrac{1}{n}\), n ∈ N}

This is read as x is such that x =\( \dfrac{1}{n}\), where n ∈ N.

**(iii)** C = {0, 3, 6, 9, 12, ….}

{x : x = 3n, n ∈ Z^{+}, the set of positive integers}

This is read as x is such that C is the set of multiples of 3 including 0.

**(iv)** D = {10, 11, 12, 13, 14, 15}

{x : x ∈ N, 9

This is read as x is such that D is the set of natural numbers which are more than 9 but less than 16.

**(v)** E = {0}

{x : x = 0}

This is read as x is such that E is an integer equal to 0.

**(vi)** {1, 4, 9, 16,…, 100}

Where,

1^{2} = 1

2^{2} = 4

3^{2} = 9

4^{2} = 16

10^{2} = 100

So, above set can be expressed in set-builder form as {x^{2}: x ∈ N, 1≤ x ≤10}

**(vii) **{2, 4, 6, 8,….}

{x: x = 2n, n ∈ N}

This is read as x is such that the given set are multiples of 2.

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

Where,

5^{1} = 5

5^{2} = 25

5^{3} = 125

5^{4} = 625

So, above set can be expressed in set-builder form as {5^{n}: n ∈ N, 1≤ n ≤ 4}

Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.