Hello to everyone who sees this question.. I have seen a problem and it was looking very easy so I tried to solve it but something seems to go wrong..
If there are 3 sets A, B, and C where |A ∪ B ∪ C| = 34, |C ∩ B ∩ A| = 2,
|A ∩ B| = 4, |A ∩ C| = 4, |A| = 16, |B| = 7, |C| = 17. What is the value of |B ∩ C| ?
I have tried by the Inclusion-Exclusion principle
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|
-> 34 = 16 + 7 + 17 - 4 - 4 - |B ∩ C| + 2
-> 34 = 34 - |B ∩ C|
-> 0 = |B ∩ C|
However it is stated that |C ∩ B ∩ A| = 2.. Thanks !!