I am suppose to find the number of integers from 1 to 1000 inclusive which are multiples of 3 or 7 or 12:
The answer I got was 414 however, the answer stated on the answer sheet provided is 428. Can anybody explain to me why is it 428?
My working is as shown:
$\left|A\bigcup B\bigcup C\right|=\left|A\right|+\left|B\right|+\left|C\right|-\left|A\bigcap B\right|-\left|B\bigcap C\right|-\left|A\bigcap C\right|-\left|A\bigcap B\bigcap C\right|\:=333\:+142\:+83\:-47-83-11-3\:=\:414$
Appreciate any help!