# Relations (Relation inside a Relation)

1. Dec 7, 2015

### XodoX

I have a question about what I would call a relation inside a relation. Like:

A={1,2,3) and B={a,b,c}

R1={(a,1) ,(a,3), (b,2), (c,1,), (c,3) }

R2={(a,a), (b,a), (b,c), (c,a) }

R3=R1R2

Like this. I have 2 regular relations. Then I form another relation using these 2. How do I do that? Like if you want to map it or show their common sets.
I would say there's none.

2. Dec 7, 2015

### Staff: Mentor

You have to define what "R1R2" is supposed to mean. The answer will be completely dependent on that definition.

3. Dec 7, 2015

### micromass

Staff Emeritus
Do you mean $R_1\circ R_2$?

4. Dec 23, 2015

### HallsofIvy

Staff Emeritus
It looks like you mean the "composition", the $R_1 \circ R_2$ that micromass suggested. If so then it would be given by;
Since $R_2$ contains (a, a) while $R_1$ contains (a, 1) and (a, 3), $R_3$ contains both (a, 1) and (a, 3). Since $R_2$ contains (b, a) while $R_1$ contains (a, 1) and (a, 3), $R_3$ contains (b, 1) and (b, 3). Since $R_2$ contains (b, c) while $R_1$ contains (c, 1) and (c, 3), $R_2$ contains (b,1) and (b, 3)- but we already have those. Since $R_2$ contains (c, a) while $R_1$ contains (a, 1) (a, 3) $R_3$ contains (c, 1) and (c, 3).

$R_3$= {(a, 1), (a, 3), (b, 1), (b, 3), (c, 1), (c, 3)}.

Last edited by a moderator: Dec 23, 2015