# Indicator function

1. Nov 22, 2014

### 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 )

2. Nov 23, 2014

### gopher_p

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

3. Nov 23, 2014

### 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