1. Define a set G as follows: G contains the Boolean variables po- P1 P2,...; for all fi.f2 G, G contains the propositional formulas fi, (fi v f2), and (fi f2); nothing else belongs to G. USE STRUCTURAL INDUCTION to prove that for every f G, there exists f' E G such that f and f' are logically equivalent, and f' does not contain the symbol "m". (Recall that propositional formulas fi and f2 are logically equivalent iff fi and f2 evaluate to the same value, no matter how their variables are set.) In your proof, clearly identify the following elements: the predicate; the base case(s); the inductive hypothesis (I.H.); where you used the I.H. in your proof of the inductive step. 1. Define a set G as follows: G contains the Boolean variables po- P1 P2,...; for all fi.f2 G, G contains the propositional formulas fi, (fi v f2), and (fi f2); nothing else belongs to G. USE STRUCTURAL INDUCTION to prove that for every f G, there exists f' E G such that f and f' are logically equivalent, and f' does not contain the symbol "m". (Recall that propositional formulas fi and f2 are logically equivalent iff fi and f2 evaluate to the same value, no matter how their variables are set.) In your proof, clearly identify the following elements: the predicate; the base case(s); the inductive hypothesis (I.H.); where you used the I.H. in your proof of the inductive step