Let  $A=\{x\in R:|x+1|<2\}$ and $B=\{x\in R:|x-1|\ge 2\}$  . Then which one of the following statements is not true?

 $A:-2<x+1<2;B:x-1\le -2orx-1\ge 2$

$$\begin{gathered} -3<x<1 x\le -1 or x\ge 3 \\ A:x\in (-3,1) B:x\in (-\infty -1)U(3,\infty ) \\ B-A=R-(-3,3) \end{gathered}$$