Recently I am working on my course Computability and Logic by Boolos, Burgess, and Jeffrey. I have some confusion on the conception of model and thus I cannot finish my homework well, and there is an exercise described like this:
"For each m and n indicate how to write down a sentence $D_(mn)$ (mn stands for the subscript for D) that is true in a model of Eq if and only if there are at least m equivalence classes with exactly n elements. " (Eq means the equivalence relation, a model of a set of sentences is any interpretation in which all sentences in the set are true) enter image description here
I do not know how to prove it, maybe I shall express $D_(mn)$ specifically? Can anyone give me a hint or a proof of this problem?