hw1 - MCS4653, Theory of Computation Homework Assignment 1,...

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

View Full Document Right Arrow Icon
MCS4653, Theory of Computation Homework Assignment 1, Due 9/15/03 Name Student ID Page 1 1. (Sudkamp 1.2) Let X = { a,b,c } and Y = { 1 , 2 } . a) List all the subsets of X . b) List the members of X × Y . c) List all total functions from Y to X . 2. (Sudkamp 1.3) Give functions f : N N that satisfy a) f is total and one-to-one but not onto. b) f is total and onto but not one-to-one. c) f is not total, but is onto. 3. (Sudkamp 1.17) Prove that the set of real numbers in the interval [0 , 1] is uncountable. Hint: Use the diag- onalization argument on the decimal expansion of real numbers. Be sure that each number is represented by only one infinite decimal expansion.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MCS4653, Theory of Computation Homework Assignment 1, Due 9/15/03 Name Student ID Page 2 4. (Sudkamp 1.41) Using the tree below, give the values of each of the items in parts ( a ) to ( e ). x 14 x 10 x 5 x 6 x 11 x 7 x 2 x 3 x 8 x 12 x 15 x 16 x 13 x 9 x 4 x 1 a) the depth of the tree b) the ancestors of x 11 c) the minimal common ancestor of x 14 and x 11 , of x 15 and x 11 d) the subtree generated by x 2 e) the frontier of the tree 5. (Sudkamp 1.42) Prove that a strictly binary tree with n leaves contains 2 n-1 nodes....
View Full Document

This note was uploaded on 02/22/2012 for the course CS 480 taught by Professor John during the Spring '12 term at Michigan State University.

Page1 / 2

hw1 - MCS4653, Theory of Computation Homework Assignment 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