First order logic, build a model to prove a formula.

Question

This is a homework question, and my mind is working a little backwards today. So I'm asking for help on a easy question, so that I can unravel the harder ones on my own.

I need to build a model for a formula so that it become true, the domain we will be using is {1,2}

∀x∀yRxy

Now I can do the oposite and prove the formula wrong by interpeting the relation symbol R as Ø, as one example. I can't make a bigger-than formula because the set in constrained to {1,2}

Anyone got a hint?

Hope I made it clear enough

Answer 1

Brett Frankel said everything in a comment:

If I understand what you're asking correctly, and you are using the language $\{R\}$, you have no choice but to let $R=\{1,2\}^2$. If you can convince yourself that this is the only way to make the model satisfy the formula, you've understood everything there is to say about this problem.