Question

集合A={x|},B={x||x-b|<a},若“a=1”是“A∩B≠”的充分條件，則b的取值范圍是…(   )

A.-2≤b<0                                          B.0<b≤2

C.-3＜b<-1                                        D.-1≤b<2

Answer 1

D

解析:A={x|}={x|-1<x<1},當a=1時,B={x||x-b|<1}={x|b-1<x<b+1},

若A∩B≠,則-1≤b-1<1或-1<b+1≤1,解得-2<b<2,故選D.