Question

The event (A∪ B∪C)∪ (AC∩BC∩CC) is ∅ the entire sample space S at least for some...

The event (A∪ B∪C)∪ (AC∩BC∩CC) is

∅

the entire sample space S

at least for some A, B and C, it is neither ∅ nor the entire sample space S

Please also explain.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

(A U B U C) is the event that contains all the elements in A or B or C

(Ac Bc Cc) is the event that contains all elements that are not in any of A, B and C.

Consider any particular elements. Either it is in A or B or C or it is not in any of the three. Therefore, the given event, (A U B U C) U (Ac Bc Cc) is,

the entire sample space S

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