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}
(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.