# Write the following intervals in set-builder form: (i) (- 3, 0) (ii) [6, 12] (iii) (6, 12] (iv) [- 23, 5)

**Solution:**

We will understand the open brackets and closed brackets.

- open brackets are denoted by '(' and ')' and are used when an element is NOT included in the inequality.

(i.e., they is used in case of '<' or '>')

- closed brackets are denoted by '[' and ']' and are used when an element is included in the inequality.

(i.e., they is used in case of '≤' or '≥')

Using this,

(i) (- 3, 0) = {x : x ∈ R, - 3 < x < 0}

(ii) [6, 12] = {x : x ∈ R, 6 ≤ x ≤ 12}

(iii) (6, 12] = {x : x ∈ R, 6 < x ≤ 12}

(iv) [- 23, 5) = {x : x ∈ R, - 23 ≤ x < 5}

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.3 Question 7

## Write the following intervals in set-builder form : (i) (– 3, 0) (ii) [6 , 12] (iii) (6, 12] (iv) [–23, 5)

**Summary:**

We are asked to write the given intervals in set-builder form. We found that

(i) (- 3, 0) = {x : x ∈ R, - 3 < x < 0}

(ii) [6, 12] = {x : x ∈ R, 6 ≤ x ≤ 12}

(iii) (6, 12] = {x : x ∈ R, 6 < x ≤ 12}

(iv) [- 23, 5) = {x : x ∈ R, - 23 ≤ x < 5}