CSE331 HW0 Answer

CSE331 HW0 Answer - CSE 331 Introduction to Algorithm...

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

View Full Document Right Arrow Icon
CSE 331: Introduction to Algorithm Analysis and Design Fall 2010 Homework 0 Solutions Do not turn in This homework is to refresh your memory on stuff you should have seen in CSE 191 and/or CSE 250. This homework is intended for you to start thinking about proofs again. Do not turn this one in, it will NOT be graded. 1. ( What is a proof? ) (40 points ) Consider the following “proof”: Brad Pitt has a beard Every goat has a beard Hence, Brad Pitt is a goat. State precisely where the “proof” above fails logically. Follow-up question: Can you prove that Brad Pitt is not a goat? Proof Idea : The main flaw in the proof above is that the conclusion seems to require the following statement as the second statement Everyone who has a beard is a goat. Also there is insufficient information to prove that Brad Pitt is not a goat, even though we know from “common knowledge” that Brad Pitt is not a goat. However, in problems that you solve in this course you cannot assume anything outside of what is given in the problem statement. More formally, we’ll use predicate logic to show the flaw in the proof that Brad Pitt is a goat. First, we’ll construct a few predicates which we can use to express the given statements. Let b ( x ) represent the statement “x has a beard”. Let g ( x ) represent the statement “x is a goat”. 2 Solution : The given proof, in our predicate notation, is: b ( Brad Pitt ) x ( g ( x ) b ( x )) Therefore g ( Brad Pitt ) In order to draw the conclusion g ( Brad Pitt ) from b ( Brad Pitt ), we would need the conditional statement x ( b ( x ) g ( x )). However, we don’t know that to be true, and it’s not equivalent to any of our statements, so this “proof” fails. We can, however, use a state- ment that is logically equivalent to the conditional statement we do have,
Background image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 3

CSE331 HW0 Answer - CSE 331 Introduction to Algorithm...

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