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mis problem you will be introduced to the notion of a partition of a set. The notion of a partition of a be useful for the theorem of total probability and when generalizing Bayes' Theorem in Week 6. V der the finite case only in this class. A1, A2, A3,..., An} = C be a finite collection of non-empty subsets of a set A. Then C is a partition A₁ U A₂ U A3 U... U An = A. If ij, then A₁ A₁ = 0 her words, (1) says that the union of all the sets in C is identical to A. (2) says that any two pair rent sets in C are disjoint, i.e., they have no members in common. tions are a very common way that we organize the world around us. The United States is partitic veral ways: by postal zip codes, by state boundaries, by time zones, etc. A chessboard is partitic two sets the squares that are black, and the squares that are white. Similarly, the collec {n EN n is even}, {n EN n is odd}} is a partition of N. = (a) Describe three partitions of the set of students at UCI. Verify that each collection you have described in (i) is indeed a partition by checking that the col satisfies the requirements (1) and (2) in the definition of a partition.

mis problem you will be introduced to the notion of a partition of a set. The notion of a partition of a be useful for the theorem of total probability and when generalizing Bayes' Theorem in Week 6. V der the finite case only in this class. A1, A2, A3,..., An} = C be a finite collection of non-empty subsets of a set A. Then C is a partition A₁ U A₂ U A3 U... U An = A. If ij, then A₁ A₁ = 0 her words, (1) says that the union of all the sets in C is identical to A. (2) says that any two pair rent sets in C are disjoint, i.e., they have no members in common. tions are a very common way that we organize the world around us. The United States is partitic veral ways: by postal zip codes, by state boundaries, by time zones, etc. A chessboard is partitic two sets the squares that are black, and the squares that are white. Similarly, the collec {n EN n is even}, {n EN n is odd}} is a partition of N. = (a) Describe three partitions of the set of students at UCI. Verify that each collection you have described in (i) is indeed a partition by checking that the col satisfies the requirements (1) and (2) in the definition of a partition.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(i) Describe three partitions of the set of students at UCI (ii) verify that each collection you have described in (i) is indeed, a partition by checking about the collection satisfies the requirements (1) and (2) in the definition of a partition.
In this problem you will be introduced to the notion of a partition of a set. The notion of a partition of a set will be useful for the theorem of total probability and when generalizing Bayes' Theorem in Week 6. We consider the finite case only in this class. Let {A1, A2, A3,..., An} = C be a finite collection of non-empty subsets of a set A. Then C is a partition of A if: (1) A₁ U A2 U A3 U... U An = A. (2) If ij, then A; n A, = 0 In other words, (1) says that the union of all the sets in C is identical to A. (2) says that any two pairs of different sets in C are disjoint, i.e., they have no members in common. Partitions are a very common way that we organize the world around us. The United States is partitioned in several ways: by postal zip codes, by state boundaries, by time zones, etc. A chessboard is partitioned into two sets the squares that are black, and the squares that are white. Similarly, the collection C = {{n EN n is even}, {n EN n is odd}} is a partition of N. Part (a) (i) Describe three partitions of the set of students at UCI. (ii) Verify that each collection you have described in (i) is indeed a partition by checking that the collection satisfies the requirements (1) and (2) in the definition of a partition.
Transcribed Image Text:In this problem you will be introduced to the notion of a partition of a set. The notion of a partition of a set will be useful for the theorem of total probability and when generalizing Bayes' Theorem in Week 6. We consider the finite case only in this class. Let {A1, A2, A3,..., An} = C be a finite collection of non-empty subsets of a set A. Then C is a partition of A if: (1) A₁ U A2 U A3 U... U An = A. (2) If ij, then A; n A, = 0 In other words, (1) says that the union of all the sets in C is identical to A. (2) says that any two pairs of different sets in C are disjoint, i.e., they have no members in common. Partitions are a very common way that we organize the world around us. The United States is partitioned in several ways: by postal zip codes, by state boundaries, by time zones, etc. A chessboard is partitioned into two sets the squares that are black, and the squares that are white. Similarly, the collection C = {{n EN n is even}, {n EN n is odd}} is a partition of N. Part (a) (i) Describe three partitions of the set of students at UCI. (ii) Verify that each collection you have described in (i) is indeed a partition by checking that the collection satisfies the requirements (1) and (2) in the definition of a partition.
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