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

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Extracted text: 15. If S1 and S2 are two semialgebras of subsets of 2, show that the class S1S2 := {A1A2 : A1 € S1, A2 E 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.