Let A, B, and C be any three events defined on a sample space S. Show that the operations of union and intersection are associative by proving that (a) A ∪ ( B ∪ C ) = ( A ∪ B ) ∪ C = A ∪ B ∪ C (b) A ∩ ( B ∩ C ) = ( A ∩ B ) ∩ C = A ∩ B ∩ C
Let A, B, and C be any three events defined on a sample space S. Show that the operations of union and intersection are associative by proving that (a) A ∪ ( B ∪ C ) = ( A ∪ B ) ∪ C = A ∪ B ∪ C (b) A ∩ ( B ∩ C ) = ( A ∩ B ) ∩ C = A ∩ B ∩ C
Solution Summary: The author demonstrates the verification of the Acap (Bcup C)=(A
Let A, B, and C be any three events defined on a sample space S. Show that the operations of union and intersection are associative by proving that
(a)
A
∪
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C
)
=
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A
∪
B
)
∪
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=
A
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(b)
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Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
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