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}