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  4. The number of positive integers from 1 to 1000, which are not divisible by 2, 3 or 5 are

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Q. The number of positive integers from 1 to 1000, which are not divisible by 2, 3 or 5 are

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Solution:

$n (2)=\left[\frac{1000}{2}\right]=500$
$n (3)=\left[\frac{1000}{3}\right]=333$
$n (5)=\left[\frac{1000}{5}\right]=200$
$n (2 \cap 3)=166, n (3 \cap 5)=66$
$n (5 \cap 2)=100 n (2 \cap 3 \cap 5)=33, n (2 \cup 3 \cup 5)=734$
$n \left(2^{\prime} \cap 3^{\prime} \cap 5^{\prime}\right)=1000-734=266$