已知A=｛x|√x∈N,1≤x≤10^6｝,B=｛x|x=20k,k∈z｝,則n(A-B)=?

Sol
A∩B=｛x｜√x=y∈N，x=20k，1<=x<=10^6，k∈z｝
x=y^2=20k=4*5k
x=4*5^2*m^2=100m^2
1<=x<=10^6
1<=100m^2<=10^6
100<=100m^2<=10^6
1<=m^2<=10^4
1<=m<=10^2
n(A∩B)=100
1<=x<<=10^6
1<=√x<=10^3
n(A)=1000
n(Ａ－B)=n(A)－n(A∩B)=1000－100=900