So I had two equations on two variables that were symmetrical. There were two possible solutions, let's call them $a$ and $b$ and so the solution set was $\{(a, b), (b, a)\}$, since the first variable could be any one of the solutions and then the second variable would have to be the other one. I was thinking of representing the solution set as $\{a, b\}^2$ but then I realized this would include ordered pairs such as $(a, a)$ or $(b, b)$ which are not a solution. In other words I want to express the set of ordered n-tuples without repetition.
Of course this could be extended to a series of equations with three variables and three solutions $a, b, c$ in which case I'd like to express the set $\{(a, b, c), (a, c, b), (b, a, c), (b, c, a), (c, a, b), (c, b, a)\}$.
So is there some sort of standard way of representing this using set theoretic notation? Thanks!