This preview shows page 1. Sign up to view the full content.
Unformatted text preview: a n = a n1 + 2 a n2 + 3 a n3 + 4 a n4 ]. By constructive Induction ﬁnd Natural numbers A,B such that ( ∀ n )[ a n ≤ A · B n ]. Make B as small as possible. Given that value of B , make A as small as possible. 4. (25 points). On the planet Gork the only currency they have is a 5cent coin and a 6cent coin. (a) Show that 19 cents cannot be formed using Gork Currency. (b) Show that, for all n ≥ 20, n cents can be formed using Gork Currency. 5. (25 points) Let S be the statement: If T is a full binary tree then the number of leaves is one more than the number of internal nodes. (a) Prove S by WEAK induction. (You MUST do the proof by REMOVING leaves from the tree, as done in class.) (b) Prove S by STRONG induction (as done in class). 1...
View
Full
Document
This note was uploaded on 12/04/2011 for the course CMSC 250 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
 staff

Click to edit the document details