A∪B can be expressed as the union of two mutual exclusive events in the following way: A∪B=A∪(B−AB). Express A∪B∪C in a similar way.

Lorena Lester

Lorena Lester

Answered question

2022-07-20

A B can be expressed as the union of two mutual exclusive events in the following way:
A B = A ( B A B )
Express A B C in a similar way.

Answer & Explanation

escobamesmo

escobamesmo

Beginner2022-07-21Added 18 answers

A B C = A ( A c B ) ( A c B c C ) .
The intuition is as follows. The first term (namely A), gets us all the elements of A. The second term (namely A c B) gets us all the elements in B, but leaves out those that we already got with our first term. Etc.

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