# Symmetric relation

Question: Let R be a symmetric relation on set A. Show that $$R^n$$ is symetric for all positive integers n.

My "solution":
Suppose R is symmetric,
$$\exists a,b \in A ((a,b) \in R \wedge (b,a) \in R)$$

For n=1,
$$R^1=R$$.
Next, assume that $$(a,b) and (b,a) \in R^k$$, for k a possitive integer. So $$R^{k+1}=R^k \circ R$$.

Then what?

HallsofIvy