MHB How do I solve a system of sets ?

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To solve the equation AUX = B in P(E), the solution is X = (B\A) U Y, where Y is an element of P(A). For the system with the additional condition A∩X = C, the correct interpretation is that Y should equal C, not X. The discussion emphasizes verifying that this solution aligns with the general form provided earlier. The participants confirm the logic and express gratitude for the clarification.
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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 ?
 
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It's not $X = C$, but $Y = C$ (following your general solution $X = (B\setminus A) \cup Y$). Check to see that this works.
 
Euge said:
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 !
 
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