let A={x:x belongs to R,|x|<1},B={x:x belongs to R,|x-1|>=1} and AunionB=R-D,then set D is?

a){x:1

b){x:1<=x<2}

c){x:-2<=x<=2}

d)none of these

Dear Krishna,
A={.9999 , ......... , -.99999}
B=(inf,2] U [0,-inf)
hence A U B= {inf,2] U [0,-inf) U {.9999 , ...... , -.9999}
=R-D
hence D must be {1.999 , ......1}
hence the answer is 1<=x<2 (b) ANS
Regards

but how do we get A={0.999.....0.99999)?