I need the answer as soon as possible 15. If S1 and S2 are two semialgebras of subsets of S, show that the classS1S2 := {A1A2 : A1 e S1, A2 e S2}is again a semialgebra of subsets of N. The field (o-field) generated byS1S2 is identical with that generated by Si U S2.

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Answered: 15. If S1 and S2 are two semialgebras…

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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15. If S1 and S2 are two semialgebras of subsets of 2, show that the class S1S2 := {A1A2 : A1 € S1, A2 € S2} is again a semialgebra of subsets of 2. The field (o-field) generated by S1S2 is identical with that generated by S1 U S2.