This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CSE105: Automata and Computability Theory Winter 2011 Homework #1 Due: Tuesday, January 11th, 2011 Problem 1 Let A be the set { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 } and B be the set { 1 , 3 , 5 , 7 } . a. How many elements in the set A \ B ? b. How many elements in the set A B 2 ? c. How many elements in the set 2 B (aka P ( B ) aka the powerset of B )? d. How many distinct functions exist mapping from A to B ? e. How many distinct functions exist mapping from B to A that are onto ? For the purpose of this question, assume that functions are defined on their entire domain. Problem 2 The Fibonacci sequence is defined as follows: F = 0, F 1 = 1, and, for n > 1, F n = F n 2 + F n 1 . The first few elements of the sequence are 0 , 1 , 1 , 2 , 3 , 5 , 8 , 13 ,... Let represent the golden ratio: = 1+ 5 2 1 . 618033989. Prove, by an inductive argument, that for all n 1 we have F n n 1 . Be sure to label clearly each part of your proof....
View
Full
Document
This note was uploaded on 08/31/2011 for the course CSE 105 taught by Professor Paturi during the Spring '99 term at UCSD.
 Spring '99
 Paturi

Click to edit the document details