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I someone help me to set my logic straight and help me understand the following situation.

For three I was given the following definition:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) − P(A ∩ B) − P(A ∩ C) − P(B ∩ C) + P(A ∩ B ∩ C).

I don't understand why we need to + P(A ∩ B ∩ C), instead of - P(A ∩ B ∩ C).

My reasoning are as follows:

1) I understand from other definitions that we − P(A ∩ B), − P(A ∩ C), − P(B ∩ C) from the union equation, because we would added the probability of A, B, and C twice if we don't do so.

2) Thus for P(A ∩ B ∩ C), it should follows the reason from 1), if we +P(A ∩ B ∩ C) instead of -P(A ∩ B ∩ C). Then wouldn't we added the probability of A,B, and C twice?

I tried to draw the Venn Diagram, to see if I can make some sense out of it. But that didn't help, as I don't get it at all and see any relationship at all. So please help.

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# Set Theory explaination help needed.

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