Express each of the following sets as an interval: (i) A = {x : x ϵR

1.	Express each of the following sets as an interval: (i) A = {x : x ϵR, –4 < x < 0} (ii) B = {x : x ϵ R, 0 ≤ x < 3} (iii) C = {x : x ϵ R, 2 < x ≤ 6} (iv) D = {x : x ϵ R, –5 ≤ x ≤ 2} (v) E = {x : x ϵ R, –3 ≤ x < 2} (vi) F = {x : x ϵ R, –2 ≤ x < 0}
Answer» (i) A = (-4,0) Explanation: All the points between -4 and 0 belong to the open interval (-4,0) but -4 ,0 themselves do not belong to this interval. (ii) B = [0,3) Explanation: B = {x : x ϵ R, 0 ≤ x < 3} is an open interval from 0 to 3, including 0 but excluding 3. (iii) C = (2,6] Explanation: C = {x : x ϵ R, 2 < x ≤ 6} is an open interval from 2 to 6, including 6 but excluding 2. (iv) D = [-5,2] Explanation: D = {x : x ϵ R, –5 ≤ x ≤ 2} is a closed interval from -5 to 2 and contains the end points. (v) E = [-3,2) Explanation: E = {x : x ϵ R, –3 ≤ x < 2} is an open interval from -3 to 2, including -3 but excluding 2. (vi) F = [-2,0) Explanation: F = {x : x ϵ R, –2 ≤ x < 0} is an open interval from -2 to 0, including -2 but excluding 0.

Express each of the following sets as an interval: (i) A = {x : x ϵR, –4 < x < 0} (ii) B = {x : x ϵ R, 0 ≤ x < 3} (iii) C = {x : x ϵ R, 2 < x ≤ 6} (iv) D = {x : x ϵ R, –5 ≤ x ≤ 2} (v) E = {x : x ϵ R, –3 ≤ x < 2} (vi) F = {x : x ϵ R, –2 ≤ x < 0}

Answer»

(i) A = (-4,0)

Explanation: All the points between -4 and 0 belong to the open interval (-4,0) but -4 ,0 themselves do not belong to this interval.

(ii) B = [0,3)

Explanation: B = {x : x ϵ R, 0 ≤ x < 3} is an open interval from 0 to 3, including 0 but excluding 3.

(iii) C = (2,6]

Explanation: C = {x : x ϵ R, 2 < x ≤ 6} is an open interval from 2 to 6, including 6 but excluding 2.

(iv) D = [-5,2]

Explanation: D = {x : x ϵ R, –5 ≤ x ≤ 2} is a closed interval from -5 to 2 and contains the end points.

(v) E = [-3,2)

Explanation: E = {x : x ϵ R, –3 ≤ x < 2} is an open interval from -3 to 2, including -3 but excluding 2.

(vi) F = [-2,0)

Explanation: F = {x : x ϵ R, –2 ≤ x < 0} is an open interval from -2 to 0, including -2 but excluding 0.