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

[vandanak]

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

 

[gopher_p]

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 $$1_{X\cup Y}=1_X+1_Y-1_X\cdot1_Y$$

 

[vandanak]

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