7 As we’ve discussed, there is no algorithm that can decide whether a given fully quantified proposition ϕ is a theorem of predicate logic. But there are several specific types of fully quantified...

7 As we’ve discussed, there is no algorithm that can decide whether a given fully quantified proposition ϕ is a theorem of predicate logic. But there are several specific types of fully quantified propositions for which we can decide whether a given statement is a theorem. Here you’ll show that, when quantification is only over a finite set, it is possible to give an algorithm to determine whether ϕ is a theorem. Suppose that you are given a fully quantified proposition ϕ, where the domain for every quantifier is a finite set—say S = {0, 1}. Describe an algorithm that is guaranteed to figure out whether ϕ is a theore