Ω:sample space F:set E:belongs For an σ-algebra

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The discussion focuses on the properties of σ-algebras in relation to sample spaces and sets. It establishes that for a σ-algebra F, the sample space Ω belongs to F, the complement of any set A in F also belongs to F, and the unions of sets Ai indexed by {1,n} are included in F. The user seeks assistance in proving that the intersections of sets Ai also belong to F, utilizing De Morgan's Law, which states that complements swap unions and intersections.

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Ω:sample space
F:set
E:belongs

For an σ-algebra the following statements are true:
1)Ω E F
2)If A E F then Acomplement E F
3)the unions of Ai i={1,n} E F

Now i must prove that the intersections of Ai i={1,n} E F
with the De Morgans Law

Can you help me?
 
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complements swap union and intesection...
 

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