### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Class Note for PHIL 110 at UMass(15)

### View Full Document

## 14

## 0

## Popular in Course

## Popular in Department

This 8 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Massachusetts taught by a professor in Fall. Since its upload, it has received 14 views.

## Similar to Course at UMass

## Popular in Subject

## Reviews for Class Note for PHIL 110 at UMass(15)

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15

INTRO LOGIC CHAPTER 3 DAY 04 VALIDITY IN SENTENTIAL LOGIC 1 3 Schedule for Unit 1 Validity in General Day1 Intro an argument is valid an argument is invaicl J D 2 Ch t 1 if and only if if and only if ay ap er it is Mpossible for it is possible for Day 3 Chapter 2 the conclusion to be the conclusion to be 40 of false false Day 4 Chapter 3 Exam 1 while while Day 5 Chapter 4 the premises are true the premises are true 60 of Day 6 Chapter 4 Exam 1 Day 7 Chapter 4 Day 8 EXAM 1 Validity in Sentential Logic Exampe1 an argument is valid an argument is analid If an argument form has 2 atomic sentences if and only if if and only if then there are 4 cases 4 22 there is there is m case at least one case R S in which in which the premises are true the premises are true case 1 T T and and case 2 T F the conclusion is the conclusion is false false case 3 F T case 4 F F 5 What is a Case Example 2 A case is a If an argument form has 3 atomic sentences 3 possible combination of truthvalues the there are 8 cases 8 39 2 139 assigned to the atomic formulas Q R 3 case 1 T T T case 2 T T F case 3 T F T case 4 T F F case 5 F T T case 6 F T F case 7 F F T case 8 F F F Example 1 Modus Tollens premise premise I conclusion if R then S not 8 I not R R a S MS I NR Example 2 Evil Twin of Modus Tollens TruthTable case R S R a S MS I NR 1 T T T F F 2 T F F T F 3 F T T F T 4 F F T T T Is there a case in which the premises are all true No butthe conclusion is false Is the argument form valid or invalid VALID 10 premise premise I conclusion if R then S not R I not 8 R a S NR I NS 11 Counterexample ithhen S notR InotS ifl live in Boston I don39t live I don39t live then I live in Mass in Boston in Mass T T F 12 TruthTable TruthTable case R S RaS NR INS case R S RaS R IS 1 T T T F F 1 T T T T T 2 T F F F T 2 T F F T F 3 F T T T F 3 F T T F T 4 F F T T T 4 F F T F F Is there a case in which the premises are all true YES Is there a case in which the premises are all true No butthe conclusion is false butthe conclusion is false Is the argument form valid or invalid INVALID Is the argument form valid or invalid l VALID l 13 15 Example 3 Example 4 Modus Ponens Evil Twin of Modus Ponens premise premise I conclusion premise premise I conclusion if R then S R I S if R then S S I R R a S R I S R a S S I R 14 16 Counterexample Example 5 Modus Tollendo Ponens disjunctive syllogism premise premise I conclusion R or S not R I S R v S NR I S 19 if R then S S I R ifl live in Boston I live in I live in then I live in Mass Mass Boston T T F 17 TruthTable case R S R a S S I R 1 T T T T T 2 T F F F T 3 F T T T F 4 F F T F F Is there a case in which the premises are all true YES butthe conclusion is false Is the argument form valid or invalid INVALID 18 TruthTable case R S R v S NR I S 1 T T T F T 2 T F T F F 3 F T T T T 4 F F F T F Is there a case in which the premises are all true No but the conclusion is false Is the argument form valid or invalid VALID 20 Example 6 Evil Twin of MTP premise premise I conclusion R or S R I not 8 R v S R I NS 21 Example 7 notR I notRand S RampS 23 TruthTable case R S R v S R I NS 1 T T T T F 2 T F T T T 3 F T T F F 4 F F F F T Is there a case in which the premises are all true YES butthe conclu5ion IS false Is the argument form valid or invalid INVALID 22 TruthTable R I R amp s F T F T T T F T T T F F T F T F F T T F T F F F Is there a case in which the premises are all true No but the conclusion is false Is the argument form valid or invalid VALID 24 Example 8 not R and 8 not R RampS 25 Logical Equivalence Two formulas are logically equivalent if and only if they have the same truthvalue no matter what in every case 27 TruthTable ampS I aaam mm i li lm 111a marme aamm mmaam butthe conclusion is false Is there a case in which the premises are all true YES Is the argument form valid or invalid INVALID 26 Examples 7 and 8 ZOMBIE REASONING not R and S not R and not 8 3 not RorS not Ror notS 3 IT IS JUST LIKE MATH x y2 x2 y2 a x y xx y 3 28 TruthTable for 7 Valid Equivalence 1 RampSII R amp 3 F T T T F T F F T T T F F F T F T F T F F T T F F F T T F F F T F T T F T Do the formulas match in truth value T NO T T Are the two formulas logically equivalent T NO T 30 TruthTable for 8 RVSII R v 3 F T T T F T F F T F T T F F T T T F F F T T T F T F T T F F F T F T T F T Do the formulas match in truth value T NO T T Are the two formulas logically equivalent T NO T 31 RampSII R v 3 F T T T T T F F T T T F F F T T T F T F F T T F T F T T F F F T F T T F T Do the formulas match in truth value T YES T T Are the two formulas logically equivalent T YES T 32 Valid Equivalence 2 RVSII R amp 3 F T T T F T F F T F T T F F T F T F F F T T T F F F T T F F F T F T T F T Do the formulas match in truth value T YES T TArethe two formulas logically equivalent T YES T 33

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.