Question

how many integers from 1 to 2009 are divisible by 5, or by 7, or by 9?

Answer 1

is there an equation to find this out or do we just have to find out this?

Answer 2

I got 785 by brute force.

Table[
{! Mod[n, 5] == 0 && ! Mod[n, 7] == 0 && ! Mod[n, 9] == 0}, {n, 2009}
] // Flatten

The preceding Mathematica statement produces a list of the words True and False, 2009 words in length. True means that neither 5, 7 or 9 divide n and False means that at least one of the thee divides n.

The list was pasted into EditPadPro where it was instructed to count the number of "False" words.