Let
 $$A=\{ n : n<10,000 \& n\in \mathbb{N}\}$$
 $$A_3=\{ n :n \in A \& 3n\}$$
 $$A_5=\{ n :n \in A \& 5n\}$$
Hence, number of positive integers less than or equal to 10,000 which are divisible by neither 3 nor 5
$$=A_3^c\bigcap A_5^c$$
$$=(A_3\bigcup A_5)^c$$
$$=10,000(A_3\bigcup A_5)$$
$$=10,000(A_3A_5)+(A_3\bigcap A_5)$$
$$=10000\lfloor\frac{10000}{3}\rfloor\lfloor\frac{10000}{5}\rfloor+\lfloor\frac{10000}{15}\rfloor=1000033332000+666=5333$$
Yeah, your answer is correct!

This reply was modified 2 months, 3 weeks ago by Nitin Prasad.

This reply was modified 2 months, 3 weeks ago by Nitin Prasad.

This reply was modified 2 months, 3 weeks ago by Nitin Prasad.

This reply was modified 2 months, 3 weeks ago by Nitin Prasad.