How do I solve a system of sets ?

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In summary, the conversation discusses solving equations and systems in P(E), with the given elements A, B, and C. The first equation is solved as X = (B\A) U Y, where Y is an element of P(A). The second system involves A, B, and C being subsets of each other, and is solved as X = (B\A) U Y, with Y = C.
  • #1
fatineouahbi
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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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  • #2
It's not $X = C$, but $Y = C$ (following your general solution $X = (B\setminus A) \cup Y$). Check to see that this works.
 
  • #3
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 !
 

FAQ: How do I solve a system of sets ?

How do I know if a given system of sets has a solution?

The system of sets will have a solution if the sets in the system are not disjoint, meaning they have at least one element in common. If the sets are disjoint, then the system has no solution.

What is the process for solving a system of sets?

The process for solving a system of sets is similar to solving a system of equations. First, identify the variables in each set and write out the equations that represent the relationships between the sets. Then, use techniques such as substitution or elimination to solve for the variables and find the solution to the system.

Is there a specific method or algorithm for solving systems of sets?

Yes, there are several methods for solving systems of sets, including the substitution method, elimination method, and graphing method. The method used will depend on the complexity of the system and personal preference.

How do I check if my solution to a system of sets is correct?

To check if your solution is correct, you can plug the values of the variables into each equation in the system and see if they satisfy all of the equations. If they do, then your solution is correct.

Can systems of sets be solved using computer programs or algorithms?

Yes, systems of sets can be solved using computer programs or algorithms. There are various software and programming languages that have built-in functions for solving systems of sets, such as MATLAB and Python. These programs use algorithms to solve the system and provide the solution.

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