- #1
Natalie1
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Can Algebra of Sets Determine Solutions for Set Equations Like $AX=C$?
In summary, the conversation discusses how to solve an algebra of sets problem and the user asks for help and recommendations for resources. A potential solution is suggested, which involves simplifying the equation to $AX=C$ where $C\subseteq A$ and then finding $X$ as the union of $C$ and a disjoint set $B$. No further explanation or resources are provided.
- #2
MarkFL
Gold Member
MHB
- 13,288
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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. :)
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. :)
- #3
Natalie1
- 7
- 0
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.
Attachments
- #4
MarkFL
Gold Member
MHB
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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. :)
- #5
Evgeny.Makarov
Gold Member
MHB
- 2,436
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The equation simplifies to $AX=C$ where $C\subseteq A$. Therefore, $X=C\cup B$ where $B$ is any set disjoint with $A$.
- #6
Natalie1
- 7
- 0
Evgeny.Makarov said:
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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FAQ: Can Algebra of Sets Determine Solutions for Set Equations Like $AX=C$?
How do I simplify an algebra of sets expression?
To simplify an algebra of sets expression, you can use the properties of set operations such as union, intersection, and complement. Start by identifying common elements between sets and combining them using the appropriate operation. Then, use De Morgan's laws to distribute and simplify the expression further.
What is the difference between a union and an intersection in algebra of sets?
A union of two sets includes all elements that belong to either set, while an intersection only includes elements that are common to both sets. In other words, the union is the combination of two sets, while the intersection is the overlap between two sets.
How do I find the complement of a set in algebra of sets?
The complement of a set includes all elements that are not in the original set. To find the complement of a set A, you can use the universal set U and subtract the elements of A from U. This can also be written as Ac = U - A.
Can I use algebra of sets to solve word problems?
Yes, algebra of sets can be used to solve word problems that involve sets. By representing the given information in terms of sets and their operations, you can use algebraic techniques to find the solution. It is important to carefully read and understand the problem to correctly translate it into algebraic expressions.
How do I know if two sets are equal in algebra of sets?
Two sets are equal if they have the same elements. In algebra of sets, this means that the sets have the same elements and the same cardinality (number of elements). You can use set notation or a Venn diagram to compare two sets and determine if they are equal or not.