1. Let 2 (a, b, c} be the sample space.the power sot of O(c) Show that F= {0, 2, {a, b}, {b, c}, {b}} is not a σ-field. Add some elementsto make it a σ-field.

Step 2: Adding elements to make F a σ-field:To ensure F is closed under complements and countable…

Answered: 1. Let 2 (a, b, c} be the sample space.…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.6: Algebraic Extensions Of A Field

Problem 9E: Construct a field having the following number of elements.

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1. Let 2 (a, b, c)} be the sample space. (a) Write down the power set of 2. (b) Construct a σ-field containing A = {a, b} and B = {b, c}. (c) Show that F= {0, 2, {a, b}, {b, c}, {b}} is not a σ-field. Add some elements to make it a σ-field..
5. Let p be a prime number and let Fp denote the field with p elements, Fp = {0, 1,...,p-1}, equipped with the operations of arithmetic modulo p. Consider the action of SL2 (Fp) on F2 defined by TA(V) := Av. Show that the orbit of the vector (1) is the set of all nonzero vectors in F2. How many elements belong to the orbit and stabiliser of this vector? Use these answers to calculate |SL2(Fp)|.
Section 48 number 18

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1. Let 2 (a, b, c} be the sample space. the power sot of O (c) Show that F= {0, 2, {a, b}, {b, c}, {b}} is not a σ-field. Add some elements to make it a σ-field.