Chapter A.1, Problem 2E

(a)

To determine

Is the statement $0<x<4$ necessarily true for the condition $2<x<6$?

(b)

To determine

Is the statement $0<x-2<4$ necessarily true for the condition $2<x<6$?

(c)

To determine

Is the statement $1<\frac{x}{2}<3$ necessarily true for the condition $2<x<6$?

(d)

To determine

Is the statement $\frac{1}{6}<\frac{1}{x}<\frac{1}{2}$ necessarily true for the condition $2<x<6$?

(e)

To determine

Is the statement $1<\frac{6}{x}<3$ necessarily true for the condition $2<x<6$?

(f)

To determine

Is the statement $\left|x-4\right|<2$ necessarily true for the condition $2<x<6$?

(g)

To determine

Is the statement $-6<-x<2$ necessarily true for the condition $2<x<6$?

(h)

To determine

Is the statement $-6<-x<-2$ necessarily true for the condition $2<x<6$?