Express each of the following sets as an interval:
(i) $A=\{x: x \in R,-4 (ii) $B=\{x: x \in R, 0 \leq x<3\}$ (iii) $C=\{x: x \in R, 2 (iv) $D=\{x: x \in R,-5 \leq x \leq 2\}$ (v) $E=\{x: x \in R,-3 \leq x<2\}$ (vi) $F=\{x: x \in R,-2 \leq x<0\}$
(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: $B=\{x: x \in R, 0 \leq x<3\}$ 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.