
Formalization of tuples
Hello,
I'm trying to formalize some properties of tuples and I find some problems for relating the elements of the tuple.
I have the tuple at time defined as , where:
 is a set of elements at time
 is a set of elements at time
 is a set of elements at time
 , where if and are related.
 , where if and are related.
 , where if and are related.
Now, I want to represent that: if at time , there is a relationship that is 1 between and , and a relationship that is 1 between and , then it must exists a relationship between and that is also 1. I don't really know how to write it. I first tried:
I think this option is not mathematically correct because is not a set. May the next option be more correct??
I don't know how to say it. I would be very grateful If you could help me.
Thank you.

Quote:
Originally Posted by
klendo
This seems correct. You may need to quantify this statement over all a, b, c, and possibly t.
I'd suggest using relations instead of functions q, r, s (they are characteristic functions of relations).

Thank you for your answer emakarov.