The number of integers from 1 to 1000 which a | vedclass

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(B) Let $A$ be the set of integers from $1$ to $1000$ divisible by $2$,and $B$ be the set of integers from $1$ to $1000$ divisible by $3$. We need to

Vedclass · Accepted Answer

$667$

Vedclass · Answer

(B) Let $A$ be the set of integers from $1$ to $1000$ divisible by $2$,and $B$ be the set of integers from $1$ to $1000$ divisible by $3$. We need to find $|A \cup B| = |A| + |B| - |A \cap B|$. $|A| = \lfloor \frac{1000}{2} floor = 500$. $|B| = \lfloor \frac{1000}{3} floor = 333$. $|A \cap B|$ is the number of integers divisible by both $2$ and $3$,i.e.,divisible by $	ext{lcm}(2, 3) = 6$. $|A \cap B| = \lfloor \frac{1000}{6} floor = 166$. Therefore,$|A \cup B| = 500 + 333 - 166 = 667$.

The number of integers from $1$ to $1000$ which are divisible by $2$ or $3$ is

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