# S â—¦ R : duplicate relations?

RR = {(2,1),(2,2)}\{(2,1),(2,2)\}

SS = {(1,2),(2,2)}\{(1,2),(2,2)\}

S∘RS \circ R = {(2,2),(2,2)}

Is the answer then {(2,2),(2,2)} or {(2,2)}
I couldn’t find anything about removing duplicates relations,
but it makes more sense that way. Especially when put in a matrix.

Unless this is allowed

S∘RS \circ R =
[0002]\begin{bmatrix}
0 & 0 \\
0 & 2 \\
\end{bmatrix}

=================

You write only (2,2)(2,2).
– Antioquia3943
Oct 21 at 1:55

My method is then, to get all the relations. And then remove the duplicates? Or should i be checking if it exists already, if it does, don’t write it?
– Grimchester
Oct 21 at 1:59

You remove the duplicates. Its like when you have a set, name A={x}A=\{x\}. You can write A={x,x}A=\{x,x\} but is redundant.
– Antioquia3943
Oct 21 at 2:06

Okey thanks. My math book only had examples without any chance of duplicates, so when it happened that I got duplicates I wasn’t sure what the correct answer was 🙂
– Grimchester
Oct 21 at 2:09

=================

=================