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Suppose that |A| = |B| = |C| = 100, |A n B| = 60, |A n...

Suppose that |A| = |B| = |C| = 100, |A n B| = 60, |A n C| = 50, |B n C| = 40, and |A U B U C| = 175. How many elements are in A n B n C?

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Answer #1

|A U B U C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|
175 = 100 + 100 + 100 - 60 - 50 - 40 + |A ∩ B ∩ C|
175 = 300 - 150 + |A ∩ B ∩ C|
175 = 150 + |A ∩ B ∩ C|
|A ∩ B ∩ C| = 175 - 150
|A ∩ B ∩ C| = 25
Answer: 25
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