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|.

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|.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.1: Sets And Geometry

Problem 11E: For the sets gives in Exercise 9, is there a distributive relationship for union with respect with...

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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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