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I am teaching myself the discrete math using the "Discrete Mathematics

Lecture Notes, Yale University, Spring 1999".

And I don't how to prove the practice question below:

Prove that |A∪B|+|A∩B| = |A|+|B|.

The text book provide answer like below:

The common elements of A and B are counted twice on both sides; the elements in

either A or B but not both are counted once on both sides.

But I think it may be some mathematical way to prove that.

If someone can give me a hand that will be very appreciated.

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# How to prove that |A∪B|+|A∩B| = |A|+|B|.

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