Tic: Relations & Sets: A Subset Possibility?

[StIgM@]

Hello guys,
I am new to this forum.

I have a question:
A relation can be subset of some other relation?

For example? I have the relations
X: A <---> B
Y: B <---> C
Z: A <---> C

X relational composition Y can be a subset of Z (if Z contains all the pairs of the composition)

Thanks in advance for your help

StIgM@

 

[disregardthat]

A binary relation is a set R of pairs (x,y) such that (x,y) is in R if an only if x is related to y. If x and y are related we write xRy. In general, a n-ary relation in general is a set of n-tuples. A subset of a relation R is merely a subset of the set R.

In set theory we usually define a relation as an ordered triple (A,B,R), where R is a subset of A x B.

 

[StIgM@]

Ok, I get your meaning but you didn't give an answer to my example!

Do you know if this is correct?

For example? I have the relations
X: A <---> B
Y: B <---> C
Z: A <---> C

X relational composition Y can be a subset of Z (if Z contains all the pairs of the composition)
?

 

[discrete*]

Ok, I get your meaning but you didn't give an answer to my example!

Do you know if this is correct?

For example? I have the relations
X: A <---> B
Y: B <---> C
Z: A <---> C

X relational composition Y can be a subset of Z (if Z contains all the pairs of the composition)
?

This is not really the right place to post homework-style questions. Also Jarle's post contains the answer to your question in the clever wording of the definition. Good luck, welcome to the forum!

 

[blue_raver22]

Hello and welcome to the forum!

To answer your question, yes, a relation can be a subset of another relation. In your example, the relation X composed with Y can be a subset of Z because all the pairs in the composition are also present in Z. This is known as the subset property of relations.

In general, a subset relation is a relation where every element in the first set (X) is also in the second set (Y). In terms of relations, this means that every pair in the first relation is also present in the second relation.

I hope this helps clarify your question. Let me know if you have any further questions. Happy learning!