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are fields of subsets of 2, then F1N F2 is 3.15 Prove that if F1 and F2 also a field.

are fields of subsets of 2, then F1N F2 is 3.15 Prove that if F1 and F2 also a field.

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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• Definition 3.1 A family F of subsets of a non-empty set N is called a field on N if (a) NE F; (b) if A € F, then N \ A e F; (c) if A, B e F, then AUBE F. The elements of a field are called events. The conditions of this definition can be read as follows: (a) the set of all outcomes is an event; (b) the complement of an event is an event; (c) the union of two events is an event. 3.15 Prove that if F1 and F2 are fields of subsets of N, then F1 N F2 is also a field. 3.16 Find two fields such that their union is not a field. So far we have considered examples of finite fields. There are also fields consisting of infinitely many events.
Transcribed Image Text:• Definition 3.1 A family F of subsets of a non-empty set N is called a field on N if (a) NE F; (b) if A € F, then N \ A e F; (c) if A, B e F, then AUBE F. The elements of a field are called events. The conditions of this definition can be read as follows: (a) the set of all outcomes is an event; (b) the complement of an event is an event; (c) the union of two events is an event. 3.15 Prove that if F1 and F2 are fields of subsets of N, then F1 N F2 is also a field. 3.16 Find two fields such that their union is not a field. So far we have considered examples of finite fields. There are also fields consisting of infinitely many events.
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