How Does the Indicator Function Prove 1A U (B∩C) = 1A.(1B + 1C - 1B.1C)?

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SUMMARY

The discussion centers on the proof of the equation 1A U (B∩C) = 1A.(1B + 1C - 1B.1C) as presented in the book by Corbae, Stinchcombe, and Zemam. Participants clarify that the correct formulation should be 1_{A∩(B∪C)} = 1_A·(1_B + 1_C - 1_B·1_C), derived from the properties of indicator functions for intersections and unions. The confusion arises from a potential misprint in the original equation, as the union should involve A and (B intersection C) rather than B and C. This highlights the importance of accurately interpreting mathematical notation in proofs.

PREREQUISITES
  • Understanding of indicator functions and their properties
  • Familiarity with set theory, specifically unions and intersections
  • Basic knowledge of mathematical proofs and notation
  • Experience with the works of Corbae, Stinchcombe, and Zemam
NEXT STEPS
  • Study the properties of indicator functions in detail
  • Learn about set operations, particularly union and intersection
  • Review mathematical proofs involving indicator functions
  • Examine the works of Corbae, Stinchcombe, and Zemam for further context
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Mathematicians, statisticians, and students studying probability theory or set theory who are interested in understanding indicator functions and their applications in proofs.

vandanak
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Hi Everyone,
So here is a prove given in book by Corbae S tinchcombe Zemam so can someone clear this line of prove to me that
1AU(B∩C)=1A.(1 B +1C -1B .1C )

I don't get it please help
thanks in advance
 
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vandanak said:
Hi Everyone,
So here is a prove given in book by Corbae S tinchcombe Zemam so can someone clear this line of prove to me that
1AU(B∩C)=1A.(1 B +1C -1B .1C )

I don't get it please help
thanks in advance

Seems to me that it should be $$1_{A\cap(B\cup C)}=1_A\cdot(1_B+1_C-1_B\cdot1_C)$$ which follows from $$1_{X\cap Y}=1_X\cdot 1_Y$$ and $$1_{X\cup Y}=1_X+1_Y-1_X\cdot1_Y$$
 
that means it must be misprint or something like that because union is between A and (B intersection C) and you have taken union in B and C where there was a intersection given
 

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