ps1 - Massachusetts Institute of Technology 6.042J/18.062J,...

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: Massachusetts Institute of Technology 6.042J/18.062J, Spring 11 : Mathematics for Computer Science February 2 Prof. Albert R Meyer revised Sunday 6 th February, 2011, 03:18 Problem Set 1 Due : February 11 Reading: Part I . Proofs: Introduction , Chapter 1 , What is a Proof? ; Chapter 2 , The Well Ordering Principle ; and Chapter 3 through 3.5 , covering Propositional Logic . These assigned readings do not include the Problem sections . (Many of the problems in the text will appear as class or homework problems.) Reminder : Email comments on the reading are due at times indicated in the online tutor problem set TP.2. Reading Comments count for 3% of the final grade. Problem 1. The fact that that there are irrational numbers a;b such that a b is rational was proved in Problem 1.2 of the course text. Unfortunately, that proof was nonconstructive : it didnt reveal a specific pair, a;b , with this property. But in fact, its easy to do this: let a WWD p 2 and b WWD 2 log 2 3 . We know p 2 is irrational, and obviously a b D 3 . Finish the proof that this a;b pair works, by showing that 2 log 2 3 is irrational. Problem 2. Use the Well Ordering Principle to prove that n 3 n=3 (1) for every nonnegative integer, n . Hint: Verify ( 1 ) for n 4 by explicit calculation. Problem 3. Describe a simple recursive procedure which, given a positive integer argument, n , produces a truth table whose rows are all the assignments of truth values to...
View Full Document

Page1 / 5

ps1 - Massachusetts Institute of Technology 6.042J/18.062J,...

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