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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 negation-normal form, P is equivalent to a formula in negation-normal 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 Gener-ation 2 , etc. How many ancestors do you have at Generation n , for any n 0? Give a proof using induction....
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This note was uploaded on 10/04/2009 for the course CMPSC 360 taught by Professor Haullgren during the Fall '08 term at Pennsylvania State University, University Park.
- Fall '08