Specify the domain as a list of natural numbers (e.g., 0, 1, 2). For each constant, give its denotation. For each one-place predicate, list the domain elements it applies to. For two-place predicates, list ordered pairs such as [0, 1]; for three-place predicates, ordered triples.
For each set of sentences below, provide a model in which they are all true.
Provide a counterexample to the equivalence of each pair of sentences: build a model in which one is true and the other is false.
Provide a counterexample to the validity of each argument: build a model in which the premises are all true but the conclusion is false. The negation of the conclusion appears as the last formula.