Remember that, in class, we constructed a function U, which took in a propositional formula and output a propositional f

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Remember That In Class We Constructed A Function U Which Took In A Propositional Formula And Output A Propositional F 1 (143.85 KiB) Viewed 49 times

Remember that, in class, we constructed a function U, which took in a propositional formula and output a propositional formula, defined recursively as follows. • for every proposition symbol p, U (p) = p U(-) = ¬U (6) U(A) = U(V) ● ● ● (U(p) → ¬U(y)) U (6) → U (y) U(p) → U (y) ) = ((U(¢) → U(v)) → ¬(U(6) → U($))) ● = • U(→ 4) = U ( In this exercise, you will outline part (but not all) of the inductive proof that for all formulas þ, U() is logically equivalent to . In particular, assume as your inductive hypothesis that we have two formulas, & and &, which we know to be logically equivalent to U(6) and U(4) respectively. Then, prove that U( V ) is logically equivalent to V.