How do I solve a system of sets ?

[fatineouahbi]

Let A,B and C be three elements of P(E)
1. Solve in P(E) the following equation : AUX=B
2. Let's suppose that C ⊂ A ⊂ B , solve in P(E) the following system : AUX=B and A⋂X=C

I've already answered the first question , it's X = (B\A) U Y such that Y∈P(A)
As for the second , I thought maybe X=C but I don't think it's right ?

 

[Euge]

It's not $X = C$, but $Y = C$ (following your general solution $X = (B\setminus A) \cup Y$). Check to see that this works.

 

[fatineouahbi]

It's not $X = C$, but $Y = C$ (following your general solution $X = (B\setminus A) \cup Y$). Check to see that this works.

Okay,thanks a lot !