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Southern New Hampshire University **We aren't endorsed by this school
MAT 230
Nov 9, 2023
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Figure 3.12.1: The general inclusion-exclusion principle applied to four sets. AUBUCUD| = |A|+|B|+|C| + |D| —|ANnB|-]ANC|—|ANnD|—|BNC|—|BND|—|CnND)| +|ANBNC|+|ANBND|+|ANCND|+|BNCND| —|AnBNCND| :':;,T",fT':AT'ON 3.12.6: Applying the general inclusion-exclusion principle. reeapnack:s (add the sizes of the sets) (subtract pairwise intersections) (add three-way intersections) (subtract the four-way intersectio Feedback? 1) Suppose you are using the inclusion-exclusion principle to compute the number of elements in the union of four sets. Each set has 15 Comract elements. The pair-wise intersections have 5 elements each. The 37 three-way intersections have 2 elements each. There is only one element in the intersection of all four sets. What is the size of the There are (;1) pairwise intersections, each of which has 5 union? elements. There are (g) three-way intersections, each of 37 which has 2 elements. There is only one intersection of z all four sets. eck Sh ow answer 4.15_('21)54-(§)2—1=60—6-5+4'2—1=37 CHALLENGE . : : - | ACTIVITY 3.12.1: The general inclusion-exclusion principle. Jump to level 1 Given two sets: A and B. A has 5 elements. B has 9. A and B share 3 elements. How many elements are there in total? Feedback? B ~-J~0-
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