Question

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).

Answer 1

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

Answer 2

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?

Answer 3

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

Answer 4

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

Answer 5

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