Write the following as intervals : (i) {x : x ∈ R, -3 < x < 6} (ii

1.	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» (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]

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»

(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]