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# Sets, Finding missing numbers watch

1. Ok i have some questions like the one below but im not sure what the method is for solving them, i've had a go at doing it, I think are probably other way than using sets to solve this type of question but i need to do it using sets.

Of 46 malicious hackers, each of whom writes at least one of boot sector, para-
sitic and macro viruses (see
http://www.uk.sophos.com/virusinfo/w...s/videmys.html
for explanations) 6 only write boot sector viruses, 9 only write parasitic viruses,
and 27 will write macro viruses. How many will write boot sector and parasitic,
but not macro viruses?

My attempt

A = the set of boot sector viruses
B = the set of parastic viruses
C = the set of macro viruses

|A union B union C| = 46

|A union B union C| - |A| - |B| - |C| + |A union B|
46 - 6 - 9 - 27 + |A union B|
46 - 6 - 9 - 27 + = 4

So i have 4 left over but how do i now work out :-
|A union B| and |A union C| |B union C| as im only interested in finding
|A union B|

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