I have a question that I have tried, but it doesn't have an answer and I can't check my work. The question is:
Find out how many integers are in [100, 999] that are multiples of 2, 3, or 5.
The first thing I did was subtract 999 with 100 to get 899. I denoted 2 as P, 3 as Q and 5 as R. I made this inclusion/exclusion formula to get the answer:
N(P $\cup$ Q $\cup$ R) = N(P) + N(Q) + N(R) - N(P $\cap$ Q) - N(Q $\cap$ R) - N(P $\cap$ R) + N(P $\cap$ Q $\cap$ R)
For P, I found there to be 449 integers that divide by 2. For Q, I found there to be 299 integers that divide by 3. For R, I found there to be 179 integers that divide by 5. Combining all of these numbers, I came up with 927. For N(P $\cap$ Q), the number I found was 149. For N(Q $\cap$ R), I found the number to be 59. For N(P $\cap$ R), I found the number to be 89. I subtracted the total of these numbers with 927 to get (927 - 297) to get 630.
Did I do this correctly?