Calculating μ(A\ B) in probability space

[Addison John]

Hi @all,

I am new in learning sigma-algebra. My question is related to computing μ(A\ B). I just need the hints and ideas on how to do it, I will do it.

Let (X,Ao,μ) be a probability space. It is given that A, B and C are 3 sets such that μ(A∩B) = 3/5 , μ(A∩C) = 3/5 and μ(B∩C) = 3/5. μ(A∩B∩C) = 2/5.

How can I calculate μ(A\ B) from these? Any help will be highly appreciated. Thanks in advance.

 

[blamocur]

I would start by drawing Venn diagram for A,B,C and computing [imath]\mu[/imath] for each subset in there. In particular, it might be helpful to show first that
[math]\mu ((A\cap B) \cup (A\cap C) \cup (B\cap C)) = 1[/math]