# Write the following as intervals:

(i) {x : x ∈ R, - 4 < x ≤ 6}

(ii) {x : x ∈ R, - 12 < x < - 10}

(iii) {x : x ∈ R, 0 ≤ x < 7}

(iv) {x : x ∈ R, 3 ≤ x ≤ 4}

**Solution:**

An interval another form of writing an inequality or a set. It is represented using two types of brackets and the ends of the interval are nothing but the ends of the inequality. The two types of brackets are

- open brackets '(' and ')' and are used when the end of the interval is NOT included (i.e., they is used in case of '<' or '>')
- closed brackets '[' and ']' and are used when the end of the interval is included (i.e., they is used in case of '≤' or '≥')

Using these,

**(i)** {x : x ∈ R, - 4 < x ≤ 6} = (- 4, 6]

**(ii)** {x : x ∈ R, - 12 < x < – 10} = (- 12, - 10)

**(iii)** {x : x ∈ R, 0 ≤ x < 7} = [0, 7)

**(iv)** {x : x ∈ R, 3 ≤ x ≤ 4} = [3, 4]

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.3 Question 6

## Write the following as intervals : (i) {x : x ∈ R, – 4 < x ≤ 6} (ii) {x : x ∈ R, – 12 < x < –10} (iii) {x : x ∈ R, 0 ≤ x < 7} (iv) {x : x ∈ R, 3 ≤ x ≤ 4}

**Summary:**

We are asked to write the given sets as intervals. We found that

**(i)** {x : x ∈ R, - 4 < x ≤ 6} = (- 4, 6]

**(ii)** {x : x ∈ R, - 12 < x < – 10} = (- 12, - 10)

**(iii)** {x : x ∈ R, 0 ≤ x < 7} = [0, 7)

**(iv)** {x : x ∈ R, 3 ≤ x ≤ 4} = [3, 4]