Find the number of positive integers from 1 to 1000, which are divisible by atleast 2,3 or 5.
Let A be the no. of numbers divisible by 2.
B=no. of numbers divisible by 3.
C=no. of numbers divisible by 5.
A=[10002]=500
B=[10003]=333
C=[10005]=200
A∩B=10006]=166
B∩C=[100015]=66
A∩C=[100010]=100
A∩B∩C=[100030]=33
∴∩(A∪B∪C)=500+333+200−166−66−100+33=734