Assymetric relation?

Question

Hello I have a question about this task, if anyone had a similar problem it would help me.

The task is: Is this relation asymmetric ? $(x,y)\rho(a,b)\rightarrow x+y=a+b$

Thanks in advance !

Answer 1

Relation R is said to be asymmetric iff $~\forall p,q$ ($pRq \longrightarrow \neg (qRp))$. In our case if $(x,y)\rho(a,b)$ i.e. $x+y=a+b$, then $a+b=x+y,$ i.e. $(a,b)\rho(x,y)$. So $\rho$ is symmetric.