How to add sets? easy question?

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In summary, A+B is the set of all possible sums of elements from sets A and B, while A*B is the set of all possible products of elements from sets A and B. The correct calculations for A+B and A*B using these definitions are shown in the conversation.
  • #1
Unassuming
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Homework Statement



Let A = {-1,2,4,7}
Let B = {-2,-1,1}

Find A+B and A*B. (multiply)


Homework Equations





The Attempt at a Solution



Am I right here?

A+B = {-3,-2,0,1,2,3,5,6,8}

A*B = {-14,-8,-7,-4,-2,-1,1,2,4,7}
 
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  • #2
Sorry this is a bit confusing. I don't think you can add/multiply sets like that. For multiplication you need the cartesian product which is just [tex] (a,b) \quad a\in A, b\in B[/tex]. If you can expand and say what you mean by multiplying and adding sets then I can help a bit more.
 
  • #3
There are a number of different ways to define A+ B or A*B for sets. For example, those are often used to mean union and intersection of sets. I think what you are talking about is "z is in A+ B if and only if z= x+ y for some x in A and some y in B" and "z is in A*B if and only if z= xy for some x in A and some y in B." Assuming those are the definitions you are using, yes, what you have is correct.
 
  • #4
Ahh, so if I defined it as multiplication or addition, then that would be valid.

Define A + B = [ a + b : a in A, b in B }

Likewise for A*B. I was confused because it didn't seem natural.
 

1. How do I add sets?

To add sets, you first need to understand what a set is. A set is a collection of distinct objects. To add a set, you simply combine two or more sets into one set. This can be done by listing all the elements from both sets and removing any duplicates. Alternatively, you can use set operations such as union or intersection to add sets.

2. Is it easy to add sets?

Adding sets can be easy or challenging depending on the complexity of the sets and the method you use to add them. If the sets are simple and contain a small number of elements, then it can be easy to add them. However, if the sets are complex and contain a large number of elements, it may require more time and effort to add them.

3. Can I add sets with different types of elements?

Yes, you can add sets with different types of elements. Sets can contain any type of object, as long as each element is unique. When adding sets with different types of elements, you may need to convert them to a common type or use a specific set operation that supports different types.

4. How can I check if two sets are equal?

To check if two sets are equal, you can use the set equality operator (==) or the set method equals() in programming languages. This will compare the elements in both sets and return true if they are the same, and false if they are different. Keep in mind that the order of elements in a set does not matter, so two sets with the same elements in a different order are still considered equal.

5. What are some real-life applications of adding sets?

Adding sets is a fundamental concept in mathematics and has many real-life applications. Some examples include combining inventory lists, merging customer databases, and creating playlists in music streaming services. Sets are also used in computer science for data structures and algorithms, such as set intersection for searching common elements in two lists.

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