Sets That Share Some Elements But Not Disjoint

  • Thread starter Treadstone 71
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In summary, a "set that shares some elements but not disjoint" is a set with at least one common element with another set, but also has unique elements. It differs from a "set that shares all elements" in that the latter has all the same elements. It is possible for a "set that shares some elements but not disjoint" to have no common elements with another set. In mathematical notation, it can be represented as A ∩ B ∪ A. Studying this concept can help in understanding relationships between sets and identifying commonalities and differences, and can be applied in various fields of science to analyze data and make connections between variables.
  • #1
Treadstone 71
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Is there a special term for sets that are not contained in one another, but are not disjoint? That is, they share some elements but have elements in either that are not in the other.
 
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  • #3
"overlapping" sets.
 
  • #4
Yes! Overlapping will do. thanks.
 

1. What is a "set that shares some elements but not disjoint"?

A set that shares some elements but not disjoint is a set that has at least one common element with another set, but also has elements that are unique to the set.

2. How is a "set that shares some elements but not disjoint" different from a "set that shares all elements"?

A "set that shares all elements" is a set that has all the same elements as another set, while a "set that shares some elements but not disjoint" has at least one unique element.

3. Can a "set that shares some elements but not disjoint" have no common elements with another set?

Yes, it is possible for a "set that shares some elements but not disjoint" to have no common elements with another set. It just needs to have at least one unique element.

4. How do you represent a "set that shares some elements but not disjoint" in mathematical notation?

In mathematical notation, a "set that shares some elements but not disjoint" can be represented using the symbol ∩ to indicate the shared elements, and the symbol ∪ to indicate the unique elements. For example, if set A shares elements with set B but also has unique elements, it can be written as A ∩ B ∪ A.

5. What is the purpose of studying "sets that share some elements but not disjoint"?

Studying "sets that share some elements but not disjoint" can help in understanding relationships between different sets and identifying commonalities and differences. In various fields of science, this concept can be applied to analyze data and make connections between different variables.

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