Let Ω = {1, 2, 3, 4, 5, 6} be the sample space when we roll a die. Explain whether the following fields are field of sets or not. (a) F1 = {∅}. (b) F2 ={∅,Ω}. (c) F3 ={∅,{1,2},Ω}. (d) F4 = {∅,{1},{3},{2,3,4,5,6},{1,2,4,5,6},Ω}. (e) F5 = {∅,{1,3,5},{2,4,6},Ω}.

Let Ω = {1, 2, 3, 4, 5, 6} be the sample space when we roll a die. Explain whether the following fields are field of sets or not. (a) F1 = {∅}. (b) F2 ={∅,Ω}. (c) F3 ={∅,{1,2},Ω}. (d) F4 = {∅,{1},{3},{2,3,4,5,6},{1,2,4,5,6},Ω}. (e) F5 = {∅,{1,3,5},{2,4,6},Ω}.

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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Question

Let Ω = {1, 2, 3, 4, 5, 6} be the sample space when we roll a die. Explain whether the following fields are field of sets or not.

(a) F1 = {∅}.
(b) F2 ={∅,Ω}.
(c) F3 ={∅,{1,2},Ω}.
(d) F4 = {∅,{1},{3},{2,3,4,5,6},{1,2,4,5,6},Ω}.

(e) F5 = {∅,{1,3,5},{2,4,6},Ω}.

Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.

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