Find, if possible, the number of elements in sets A, B, and C using the given information. n(A∩B)=6, n(A∩B∩C)=4, n(B∩C)=9, n(B−A)=10, n(B∪C)=25, n(A∩C)=7, n(A∪B∪C)=28. n(A)= n(B)= n(C)=

Find, if possible, the number of elements in sets A, B, and C using the given information. n(A∩B)=6, n(A∩B∩C)=4, n(B∩C)=9, n(B−A)=10, n(B∪C)=25, n(A∩C)=7, n(A∪B∪C)=28. n(A)= n(B)= n(C)=

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 9AEXP

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Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

Find, if possible, the number of elements in sets A, B, and C using the given information.

n(A∩B)=6,

n(A∩B∩C)=4,
n(B∩C)=9,
n(B−A)=10,
n(B∪C)=25,
n(A∩C)=7,

n(A∪B∪C)=28.

n(A)=

n(B)=

n(C)=

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