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Suppose that F is an algebra on some sample space . Prove each of the following....

Suppose that F is an algebra on some sample space . Prove each of the following.

(a) the empty set is an element of F .

(b) AUBUC whenever A,B,C is an element of F .

(c) A1UA2UA3....UAn is an element of F whenever A1,A2............An is an element of F .

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