**Question:**

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) $F=\{x: x \in R,-2 \leq x<0\}$

**Solution:**

(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.