设全集U=A∪B={x∈N*|lgx<1},若A∩∁UB={m|m=2n+1,n=0,1,2,3,4},则集合B= _ .
问题描述:
设全集U=A∪B={x∈N*|lgx<1},若A∩∁UB={m|m=2n+1,n=0,1,2,3,4},则集合B= ___ .
答
∵U=A∪B={x∈N*|lgx<1}={x∈N*|x<10}={1,2,3,4,5,6,7,8,9},
又∵A∩∁UB={m|m=2n+1,n=0,1,2,3,4}={1,3,5,7,9},
∴∁UB={1,3,5,7,9},
∴B={2,4,6,8},
故填:{2,4,6,8}.