×

### Let's log you in.

or

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

×

or

## Discrete math indroductory week and beginning of lesson one

by: Aaron Maynard

52

1

4

# Discrete math indroductory week and beginning of lesson one CS 2305

Marketplace > ComputerScienence > CS 2305 > Discrete math indroductory week and beginning of lesson one
Aaron Maynard
UTD
GPA 3.5

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

×
Unlock Preview

These notes cover the start of the section over proposition. In the introductory (14th) week, we learned about the symbols and meaning of common propositions. In week of January 21st, we started co...
COURSE
Discrete Math for Computing I
PROF.
Timothy Farage
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
Math, Discrete math, Computer Science, Computer Science I, University of Texas at Dallas
KARMA
25 ?

## Popular in ComputerScienence

This 4 page Class Notes was uploaded by Aaron Maynard on Saturday January 16, 2016. The Class Notes belongs to CS 2305 at a university taught by Timothy Farage in Spring 2016. Since its upload, it has received 52 views.

×

## Reviews for Discrete math indroductory week and beginning of lesson one

×

×

### 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: 01/16/16
Discreet Math for Computing Aaron Maynard Timothy Farage January 14 , 2016 There are two parts to math. MATH LOGIC SET THREORY Fermat's Last Theorem: + n n n Let A, B, C, N € Z exist such that if A + B = C , then n ≤ 2 LOGIC Definition: A proposition is a statement "This is either True or False". Examples 2 + 3 = 7 True All cats have hearts True X + 2 = 7 False “There is an ‘x’ such that ‘x + 2 = 7” True Logic Variables are either True (1) or False (0) It is traditional to use variables such as P, Q, R1 o2 Pn, P , P . Logical Operators (Boolean Operators) Also known as an unary operator, only deals with one proposition. P !P (not P) 0 1 1 0 Binary Operators  PVQ, pronounced "P or Q" or "P or Q or Both”  P ΛQ, pronounced "P and Q"  P⊕Q / {P xor Q, pronounced "P x or Q" or "P or Q but NOT both"  P<->Q, pronounced "P if and only if Q"  P->Q, pronounced "If P then Q" or "P implies Q" Discreet Math for Computing Aaron Mthnard Timothy Farage January 14 , 2016 Truth Table for the Binary Operators P Q PVQ P ΛQ P⊕Q P<->Q P->Q 0 0 0 0 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 1 Side Notes from Class  Example of P<->Q: o Two sides of a triangle are equal if and only if the angles opposite those sides are equal. o If two sides of a triangle are not equal then the angles opposite those sides are not equal.  P is called the antecedent, Q is called the consequence / conclusion. Discreet Math for Computing AarothMastard Timothy Farage January 19 -21 , 2016 Compound Proposition Definition: Using multiple propositions with apparition. P -> (Q V R) P Q R ( Q V R ) P -> ( Q V R ) 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 If every circumstance is true, then the compound proposition is known as an example of "Tautology" A logical expression that is true for any values of its variables is said to be tautology. ( P Λ Q ) Λ (P -> Q) P Q PΛQ P->Q (PΛQ) Λ (P- >Q) 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 1 0 A compound proposition that is false for all values of its variables is known as a "contradiction". “I am that I am." Discreet Math for Computing AarothMastard Timothy Farage January 19 -21 , 2016 Math Equivalences: For any x and y, x + y = y + x x + 2 = 5 Logical Equivalences (Propositional Equivalences):  PVQ  QVP  PΛQ  QΛP  (PVQ)VR  PV(QVR)  PΛ(QVR)  (PΛQ)V(PΛR) ~P is known as “not P” Negate and Simplify: Definition: Simplifying until there are no negations except over variables. ~[(PΛQ) -> (Q->R)]  (PΛQ) Λ ~(Q->R)  (PΛQ) Λ (QΛ~R)  PΛQΛ~R Done! Converse of P -> Q If the animal is a cat, then it has four legs. Q -> P If the animal has four legs, then it is a cat. If a triangle has 2 equal sides, then it has 2 equal angles. If a triangle has 2 equal angles, then it has 2 equal sides. Contrapositive of P -> Q If you get over 90%, then you get an A. ~P -> ~Q If you get an A, then you get over 90%. Things to have memorized: P->Q <=> ~PVQ ~(P->Q) <=> P Λ ~Q - The negation of an implication is NOT an implication, it's an AND! Demorgans Laws: ~(PVQ) <=> ~P Λ ~Q ~(P Λ Q) <=> ~PV~Q

×

×

### 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

Bentley McCaw University of Florida

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Anthony Lee UC Santa Barbara

#### "I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

Jim McGreen Ohio University

#### "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."

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