Let G be a set defined as follows: if z is a propositional variable, then z G: if f1, f2 G, then f G. (fi V f2) G. and (f ^ f2) = G; nothing else belongs to G. Use structural induction to prove that for every f G, there exists f' G such that f and f' are logically equivalent, and f' does not contain a symbol. (Recall that propositional formulas fi and f2 are logically equivalent if fi and f2 evaluate to the same value, no matter how their variables are set.)