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

2015-12-03 5:30 pm
更新1:

10^6是指10的6次方

回答 (1)

2015-12-04 3:35 am
✔ 最佳答案
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


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