Understanding Relations in Mathematics

In summary, the conversation discusses properties of relations on different sets, specifically the relation between circles and the relation between recurrence relations. The properties being discussed are reflexivity, symmetry, antisymmetry, and transitivity, and the conversation includes a request to rephrase each of these properties in terms of the given sets.
  • #1
liahow
6
0
Not really understanding these concepts.

Consider the following relation on the set of all circles in the xy plane: A ~ B if and only if the center of circle A is inside circle B. Is ~ reflexive? Is ~ symmetric? Is ~ antisymmetric? Is ~ transitive? Prove answers.


Consider the following relation on the set of all recurrence relations. X ~ D if and only if all of the terms of the sequence associated with D appear in the sequence associated with X. Is ~ reflexive, symmetric, antisymmetric, transitive? Prove.
 
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  • #2
liahow said:
Not really understanding these concepts.

Consider the following relation on the set of all circles in the xy plane: A ~ B if and only if the center of circle A is inside circle B. Is ~ reflexive? Is ~ symmetric? Is ~ antisymmetric? Is ~ transitive? Prove answers.


Consider the following relation on the set of all recurrence relations. X ~ D if and only if all of the terms of the sequence associated with D appear in the sequence associated with X. Is ~ reflexive, symmetric, antisymmetric, transitive? Prove.
What have you done so far ? Do you understand the definitions ?
 
  • #3
As far as the definitions go, what we learned in our books is different from this equation. We've been given sets and told to go with those. Perhaps it's just my own ignorance, but when a problem is so dramatically phrased differently than the way I learn it, I am stuck in neutral.
 
  • #4
liahow said:
...
Consider the following relation on the set of all circles in the xy plane: A ~ B if and only if the center of circle A is inside circle B. ... Is ~ symmetric?
...
Let's look at this one. Rephrase the abstract property "symmetric" in terms of the set you are working with. In this case, it is asking "If a circle A has its center inside circle B, does it necessarily follow that circle B has its center inside circle A ?"
Do this with the rest of the questions. :smile:
 
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  • #5
hypermorphism said:
Let's look at this one. Rephrase the abstract property "reflexive" in terms of the set you are working with. In this case, it is asking "If a circle A has its center inside circle B, does it necessarily follow that circle B has its center inside circle A ?"
Do this with the rest of the questions. :smile:
Just so liahow isn't confused, the question above is for the symmetric property. A ~ B if and only if the center of circle A is inside circle B, so reflexive would just be A ~ A, or "the center of circle A is inside circle A".
 
  • #6
liahow said:
As far as the definitions go, what we learned in our books is different from this equation. We've been given sets and told to go with those. Perhaps it's just my own ignorance, but when a problem is so dramatically phrased differently than the way I learn it, I am stuck in neutral.
You were asked "what is the definition" of a relation. Please tell us what definitions you have learned, whether they are "different from this equation" or not (I don't quite understand that- you haven't cited any equations).
 

Related to Understanding Relations in Mathematics

1. What are relations in math?

Relations in math refer to the connection or association between two or more elements. In other words, it is a set of ordered pairs that show how two sets of data are related to each other.

2. What are the different types of relations in math?

There are several types of relations in math, including functional, bijective, inverse, reflexive, symmetric, and transitive relations. Each type has its own properties and characteristics that define how the elements are related.

3. What is a function in relation to math concepts?

In math, a function is a type of relation where each input has a unique output. This means that for every x-value (input), there is only one y-value (output). Functions are often represented as equations or graphs.

4. How are relations used in real-world applications?

Relations are used in various real-world applications, such as in economics, physics, and computer science. For example, in economics, supply and demand are related to each other, and in physics, the distance an object travels is related to its speed. In computer science, relations are used to represent data in databases and to determine connections between different elements.

5. Can you give an example of a non-mathematical relation?

Yes, a non-mathematical relation can be seen in the English language. For instance, the relation between a word and its definition is a type of relation. Another example is the relation between a parent and their child, where the parent is the source and the child is the target.

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