HW6 - EECS 203 DISCRETE MATHEMATICS Homework 6 Due Thursday November 1 at 4pm Put your name and discussion section number(not the meeting time on

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Unformatted text preview: EECS 203: DISCRETE MATHEMATICS Homework 6 Due Thursday, November 1 at 4pm Put your name and discussion section number (not the meeting time) on the first page of your homework. Submit your homework to (a) CTools, as a PDF file, or (b) the drop box marked “EECS 203” in room EECS 2420. If neither (a) nor (b) is possible please turn in your homework at one of the discussion sections. 1. (4 points) A rooted ternary tree is either a single vertex (which is the root) or consists of three ternary trees T 1 ,T 2 ,T 3 with roots r 1 ,r 2 ,r 3 , a new root vertex r , and edges { r,r 1 } , { r,r 2 } , { r,r 3 } . What is the maximum number of vertices in a ternary tree with height 1 h ? Your proof should be by induction. 2. (4 points) The sequence ( a ,a 1 ,... ) is defined recursively as follows: a = 0 and, for n > 0, a n = a n/ 2 for n even 1 + a ( n- 1) / 2 for n odd Prove by induction that a n is the number of 1s in the binary representation of n ....
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This note was uploaded on 12/20/2010 for the course EECS 203 taught by Professor Yaoyunshi during the Fall '07 term at University of Michigan.

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