Question

Write the following as intervals : 

(i) {x : x ∈ R, -3 < x < 6} 

(ii) {x : x ∈ R, -4 ≤ x ≤ 8} 

(iii) {x : x ∈ R, 4 < x ≤ 9} 

(iv) {x : x ∈ R, -6 ≤ x < -1}

Answer 1

(i) {x : x ∈ R, -3 < x < 6} 

-3 < x < 6 is open interval where -3 and 6 are not included. 

Hence, {x : x ∈ R, -3 < x < 6} has interval (-3, 6). 

(ii) {x : x ∈ R, -4 ≤ x ≤ 8} 

-4 ≤ x ≤ 8 is closed interval in which (-4 and 8) are included. 

Hence, interval is [-4, 8] 

(iii) {x : x ∈ R, 4 < x ≤ 9} 

4 < x ≤ 9 is semi closed interval where the interval is less than 4 and equal to 9. 

Hence, {x : x ∈ R, 4 < x ≤ 9} has interval [4, 9]. 

(iv) {x : x ∈ R, -6 ≤ x < -1} 

-6 ≤ x < -1 is semi closed interval where the interval is equal to -6 and less than -1. 

Hence, {x : x ∈ R, – 6 ≤ x < -1} has interval [-6, -1]