Do the following Inductive Proof Exercise: You might already be familiar with procedures for "driving" negations into the scopes of other functors through successive applications of DeMorgan's rule. Consider then the following claim, which can be established through logical induction: Any formula is equivalent to one in which all negations (if any) range over just single proposition letters (that is, one in which all the negations have been "driven" inside of any parentheses).
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Inductive step: Assume that any formula with n logical connectives is equivalent to one in which all negations range over just single proposition letters. We will show that this holds for a formula with n+1 logical connectives. Consider a formula F with n+1 Show more…
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