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]