# Characteristic Sets A & B: Special Name & Importance

• sutupidmath
In summary, the conversation discusses sets A and B and their properties of being mutually disjoint or one being a subset of the other. It is not clear if these sets have a special name, but they are studied in discrete math and may show up in other areas of math such as graph theory. The conversation also mentions the idea of a collection of sets with these properties and their potential significance.
sutupidmath
I was wondering if sets A and B, with the following property:

$$\mbox {Either } A\bigcap B=\emptyset \mbox{ or } A\bigcap B=A.$$

have a special name. The name per se is not that important, however, what i am asking is whether these are well known/studied sets, or if they are of any special importance/use? If yes, where could i read more abou them?

Thanks

Well, I haven't had a lot of courses on set theory, but if memory serves me right:

If the intersection of two sets is the empty set, then the two sets are said to be mutually disjoint.

If you know the intersection of two sets is equal to either set, then the two sets are the same. It's like the identity operation of intersection.

I studied them as part of my discrete math course, using Epp's Discrete Mathematics with Applications textbook.

So, A is either completely outside B or completely inside B? Hm, it might have a name but I haven't heard of one.

Casual Friday said:
If you know the intersection of two sets is equal to either set, then the two sets are the same. It's like the identity operation of intersection.

If by 'either set' you mean 'both sets' then yes.

Thanks for your replies, but unfortunately this is not what i was asking for ( i am well aware of the things you pointed out).

The question itself might be a little vague i believe.

Essentially, what i am saying is do these kind of sets show up somewhere? By somewhere i mean say graph theory(someone told me this, but had no more info).

In other words, say, like fibonacci sequences that show up in many places in math, do these kind of sets have 'alike' properties?

Thanks!

Just to make this clear. Are you saying that the condition you're placing on these two sets is that they must either be multually exclusive or else one be a subset of the other?

If $A \bigcap B = \emptyset$
then A and B are disjoint.
If $A \bigcap B = A$
then A is contained in B (A is a (proper) subset of B).

Other than that, I don't think there are any special names.

Mark44 said:
Other than that, I don't think there are any special names.

Yes but you can certainly imagine a physical meaning to that combination of set conditions. If I were to give it a name I would call it the "you're either all in or you're all out" condition. Or what was it that George W Bush was saying to (potential) ally nations after 911, "you're either with us or you're against us". Maybe we could call it the GWB relation, or the GWB condition. :)

I am not really interested on their 'name' per se, but more on what they could possibly represent.

To be more precise, if we have a collection of sets $$\{A_i\}$$ such that for any two sets $$A_i,A_j$$ the property i have described holds, i am wondering what could this collection of sets represent? If it does? That is, are such collection of sets of any particular importance?

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## What are characteristic sets A & B?

Characteristic sets A & B are two distinct groups of traits or features that are used to classify or identify something. These sets are often used in scientific research to categorize different species, organisms, or objects based on their unique characteristics.

## How are characteristic sets A & B different?

Characteristic set A and B are different in terms of the traits or features that they include. Set A may focus on physical characteristics, while set B may focus on behavioral characteristics. Additionally, the importance or relevance of these sets may vary depending on the specific research or study being conducted.

## What is the special name associated with characteristic sets A & B?

The special name associated with characteristic sets A & B is often referred to as a "taxon." This term is used to describe the group or category that an organism or object belongs to based on its unique features and characteristics.

## Why are characteristic sets A & B important in scientific research?

Characteristic sets A & B are important in scientific research because they allow scientists to classify and organize different species or objects based on their unique traits and features. This helps researchers to better understand the relationships between different organisms and their environments, and can also aid in the discovery of new species or objects.

## How are characteristic sets A & B used in real-world applications?

Characteristic sets A & B have a variety of real-world applications, such as in medicine, agriculture, and conservation efforts. By understanding the unique characteristics of different organisms, scientists can develop new treatments or cures for diseases, improve crop yields, and protect endangered species.

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