MHB Can Algebra of Sets Determine Solutions for Set Equations Like $AX=C$?

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The discussion centers on solving the equation $AX=C$ using the algebra of sets. Participants emphasize the importance of sharing progress to receive effective help. The equation simplifies to $X=C\cup B$, where $B$ is a disjoint set with $A$. The user seeks guidance on applying set theory laws and requests recommendations for books or resources on the topic. Overall, the conversation highlights the need for foundational knowledge in set theory to tackle such equations effectively.
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How would I solve this using the algebra of sets?

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Re: Help me please, how to solve this in algebra of sets?

Hello, Natalie! (Wave)

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

I have also edited your post to include the question in the body. We do ask that the complete question be in the post rather than in the title of the thread only. :)
 
I don't have any idea how to solve such tasks. Thats why I ask for help. Maybe you can show the algorithm of solving it, if you know. Or, I would appreciate if you could advise me sites/books that show how to solve such equations. What should I do? I have no idea how to solve it, that's why I'm asking for help. Please, please help me. I know only laws View attachment 5283, but how to apply them? My progress is only in that I know that I must use De Morgan law here.
 

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I never studied set theory, but there are folks here who have, and now knowing where you stand with the problem, they will be better quipped to give you relevant help. :)
 
The equation simplifies to $AX=C$ where $C\subseteq A$. Therefore, $X=C\cup B$ where $B$ is any set disjoint with $A$.
 
Evgeny.Makarov said:
The equation simplifies to $AX=C$ where $C\subseteq A$. Therefore, $X=C\cup B$ where $B$ is any set disjoint with $A$.

Tell me how did you solve it? Can you recommend me books (in english, or in russian), that explain such kind of equations?
 
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Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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