×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

43

0

3

# MATH REASONING MATH 310

UW
GPA 3.76

Alexandra Nichifor

These notes were just uploaded, and will be ready to view shortly.

Either way, we'll remind you when they're ready :)

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

COURSE
PROF.
Alexandra Nichifor
TYPE
Class Notes
PAGES
3
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 3 page Class Notes was uploaded by Addison Beer on Wednesday September 9, 2015. The Class Notes belongs to MATH 310 at University of Washington taught by Alexandra Nichifor in Fall. Since its upload, it has received 43 views. For similar materials see /class/192055/math-310-university-of-washington in Mathematics (M) at University of Washington.

×

## Reviews for MATH REASONING

×

×

### What is Karma?

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

Date Created: 09/09/15
Math 310 09262008 Chapter 1 continued Last time we discussed de nitions Tip It s useful to keep a list of main de nitions and results as we go 11 Statements Propositions and predicates De nition A proposition is a sentence which is at least potentially either true or false Examples but not Denote by P Q etc De nition A predicate is a sentence that can be either true or false depending on the values assigned to some of its variables For example Denote by Pn Qx y etc orjust P Q etc We refer to either propositions or predicates as statements They are the basic building blocks of logic We can combine various statements to form new ones via logical connectives III Logical Connectives Or And Not a Disjunction V OR Caution in math OR inclusive 01 Truth Table P PV F T F F De nition The disjunction P V Q of two statements P and Q is a statement which is false precisely when both P and Q are false and it s true otherwise b Conjunction A And Truth Table P De nition c Negation 39 N0t Truth Table De nition Examples 1 Let P denote the statement Susan likes bananas and Q denote the statement It rains Suppose you asked Susan and she hates bananas but you looked out the window and indeed it rains Which of the following statements are true P or Q P and Q not P not Q not P or not Q not P and not Q 2 In daily life ifI say My car is red or green what do you expect my car s color to be Now let R be the statement My car is red and G be My car is green If the logical statement R or G is true what color can my car be 3 Write out the truth tables and compare the following statements a P and not P with P or not P b not P or not Q with not P and Q c not P and not Q with not P or Q d P and P and Q with P and P and Q e not P and Q or R with not P and Q or R Chapter 2 1 Implications PgtQ If P then Q An implication is written symbolically PgtQ Usual wording Ifthen statement P implies Q If P then Q Definition The implication PgtQ is a statement which is false only when P is true and Q is false and it s true otherwise Truth Table Note P is called the and Q is called the of the implication Caution An implication shows sufficiency but not necessity it says that if P is true then Q is true However if P is false then the conclusion can be true or false without making the implication false De nition The converse of an implication P gt Q is the statement This is an entirely different statement than F gt Q but it s often mistaken for it Common erroneous argument Cows have 4 legs Fido has 4 legs Therefore Fido is a cow Write it in symbolic notation and explain what s wrong with it Let CX denote X is a cow and LX denote X has 4 legs Cows have 4 legs Fido has 4 legs Therefore Fido is is a cow II Logically Equivalent PltgtQ P if and only if Q P iff Q Definition Two statements are logically equivalent if they have precisely the same truth table Truth Table Exercises I 1 Show that PgtQ is logically equivalent to eP V Q 2 Draw the truth table for 24 ii P and QgtP To do Compare the statements from exercise 3 on the previous page and make a note which ones are equivalent Look up what is the contrapositive of an implication and how it relates to the truth value ofthe implication

×

×

### BOOM! Enjoy Your Free Notes!

×

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

Steve Martinelli UC Los Angeles

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Allison Fischer University of Alabama

#### "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!"

Steve Martinelli UC Los Angeles

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Parker Thompson 500 Startups

#### "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."

Become an Elite Notetaker and start selling your notes online!
×

### 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