Home1Review - CS 341 Automata Theory Elaine Rich Homework 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CS 341 Automata Theory Elaine Rich Homework 1 Due Thursday, September 7 at 11:00 a. m. 1) Write each of the following explicitly: a) P ({ a , b }) P ({ a , c }) b) { a , b } {1, 2, 3} c) { x : ( x 7 x 7} d) { x : 5 y ( y < 10 ( y + 2 = x ))} (where is the set of nonnegative integers) e) { x : 5 y ( 5 z (( x = y + z ) ( y < 5) ( z < 4)))} 2) Give an example, other than one of the ones in the book, of a relation on the set of people that is reflexive and symmetric but not transitive. 3) Define p to be equivalent modulo p . x p y iff x modulo p = y mod p . For example 4 3 7 and 7 5 12. Let R p be a binary relation on , defined as follows, for any p 1: R p = {( a , b ): a p b } So, for example R 3 contains (0, 0), (6, 9), (1, 4), etc., but does not contain (0, 1), (3, 4), etc. a) Is R p an equivalence relation for every p 1? Prove your answer. b) If R p is an equivalence relation, how many equivalence classes does R p induce for a given value of p ? What are they? (Any concise description is fine.) 4) Are the following sets closed under the following operations? If not, give an example that proves that they are not and then specify what the closure is. a) The negative integers under division b) The positive integers under exponentiation c) The finite sets under Cartesian product 5) Give examples to show that the intersection of two countably infinite sets can be either finite or countably infinite, and that the intersection of two uncountable sets can be finite, countably infinite, or uncountable....
View Full Document

Page1 / 3

Home1Review - CS 341 Automata Theory Elaine Rich Homework 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online