This preview shows page 1. Sign up to view the full content.
Unformatted text preview: On = {1,3, . .., 2n1}. Note that it follows that O is the set of odd numbers. (b) Prove that O = S . (Recall that this means you have to prove that S is a subset of; O and O is a subset of S . To show that S is a subset of O , use the fact that S is the smallest set satisfying S1 and S2. To show that O is a subset of S , prove by induction that On is a subset of S .) 3. [5 points] Define a function h inductively as follows. { h(1) = h(2) = 1 { h(n) = h(n1)^2 + h(n2) if n > 2. The function h grows quickly after the first few values. (a) Compute h(5). (b) Prove that for all n > 1 that the greatest common divisor of h(n) and h(n1) is 1 (i.e., h(n) and h(n1) are relatively prime). (Hint: induction is a good approach here). Page 1 of 1 Computer Science 280: Homework 3 10/18/2008 http://www.cs.cornell.edu/courses/cs280/2008sp/280hw3.html...
View
Full
Document
This note was uploaded on 10/18/2008 for the course CS 2800 taught by Professor Selman during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 SELMAN
 Computer Science

Click to edit the document details