Understanding Relations in Mathematics

[liahow]

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.

 

[hypermorphism]

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 ?

 

[liahow]

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.

 

[hypermorphism]

...
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.

 

[honestrosewater]

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.

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".

 

[HallsofIvy]

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).