Unformatted text preview: a n < 2 n for all n > 0. 6. Prove using strong induction that any propositional formula is equivalent to one that does not contain any uses of ¬ , ∧ , or ∨ . (Hint: recall Problem 9 from Assignment #1.) 7. Prove using strong induction that for any propositional formula P that is in negationnormal form, ¬ P is equivalent to a formula in negationnormal form. 8. Consider a family tree that consists of just you, your parents, their parents, etc. (no siblings). Assume you are Generation 0 , your parents are Generation 1 , your grandparents are Generation 2 , etc. How many ancestors do you have at Generation n , for any n ≥ 0? Give a proof using induction....
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 Fall '08
 HAULLGREN
 Logic, Addition, Mathematical Induction, Summation, Natural number, Penn State University

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