If n(A) = 24, n(B) = 22, n(C) = 23, n(A ∩ B) = 5, n(A ∩ C) = 9, n(B ∩ C) = 6, and n(A ∪ B ∪ C) = 51, find n(A ∩ B ∩ C).

Question

kinggeorge · Answer

By the inclusion-exclusion principle,$$|A \cap B\cap C|=|A\cup B\cup C| -|A|-|B|-|C| +|A\cap B| +|A\cap C|+|B\cap C|$$

kinggeorge · Answer

Using this, you find that $|A \cap B\cap C|= 51-24-33-23+5+9+6=-9 $
Are you sure you typed the question correctly?

anonymous · Answer

yeah, i got it the answer is 2, thanks for that formula

kinggeorge · Answer

You're welcome. I guess I did my arithmetic wrong somewhere.

kinggeorge · Answer

I see, I used 33 instead of 22. My bad.