Suppose n is greater than, or equal to 2 and a natural number. There is a pairwise disjoint set such as A1, A2, ..., An (which means that Ax∩Ay = 0 for all 1 ≤ x < y ≤ n) and the addition principle states that |A1UA2U...UAn|=|A1|+|A2|+...+|An|. Prove that that pairwise disjoint is necessary for the above statement to be true by using an example to show that if there is a set A1, A2, ..., An that  A1∩A2∩...∩An = 0 but |A1UA2U...UAn| does not equal |A1|+|A2|+...+|An|.

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