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## Discrete Math Structures

by: Mireya Heidenreich

21

0

2

# Discrete Math Structures CS 2233

Mireya Heidenreich
UTSA
GPA 3.55

Staff

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## Popular in ComputerScienence

This 2 page Class Notes was uploaded by Mireya Heidenreich on Thursday October 29, 2015. The Class Notes belongs to CS 2233 at University of Texas at San Antonio taught by Staff in Fall. Since its upload, it has received 21 views. For similar materials see /class/231398/cs-2233-university-of-texas-at-san-antonio in ComputerScienence at University of Texas at San Antonio.

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Date Created: 10/29/15
CS 2233 Fall 2008 Discrete Mathematical Structures 11 Propositional Logic Carola Wenk az7n a CS 2255 Lncrete Mathematxcal Structure W Carola Wenk Propositions De nition A proposition is a sentence that is either true I or false F but not both Examples Which of the following are propositions The Alamo is located in San Antonio 42 42 UTSA is the best school in the world 23 6 2x 6 It is warm in San Antonio ammo CS 2255 Lncrete Mathematxcal Structure W Carola Wenk z Negation 39 Definition Let p be a proposition The negation not of p denoted by up has the opposite truth value than the truth value of p Read up as not p or It is not the case that p Examples Negate the following The Alamo is located in San Antonio gtgt The Alamo is not located in San Antonio or It is not the case that the Alamo is located in San Antonio Today is Monday Truth Table P DP T F F T gtgt Today is not Monday or It is not the case that today is Monday az7n a CS 2255 Lncrete Mathematxcal Structure W Carola Wenk Conjunction Definition Let p and q be propositions The Truth Table conjunction and of p and q denoted by q pAq is true when bothp and q are true and is false otherwise Read pAq as p and q T T F F Examples Find the conjunction of p and q p It is sunny today q Today is Monday gtgt It is sunny today and today is Monday The conjunction is true on sunny Mondays TT but it is false on any nonsunny day FT or FF and it is false on any other day but Monday T F or FF ammo CS 2255 Lncrete Mathematxcal Structure W Carola Wenk 4 Disjunction v Definition Let p and q be propositions The Truth Table P disjunction inclusive or of p and q q pvq denoted bypvq is false when bothp and q T T T are false and is true otherwise T F T Readpvq as p or q F T T F F F Examples Find the disjunction ofp and q p It is sunny to ay q Today is Monday gtgt It is sunny today or today is Monday The disjunction is true on sunny Mondays TT and on Mondays FT or TT and on sunny days TF or TT It is only false on nonsunny days that are not Mondays FF az7n 8 cs 2255 Discrete Mathematical Structure W Carola Wenc 5 Exclusive Or EB Definition Let p and q be propositions The exclusive or xor of p and q denoted by p q is true when exactly one ofp and q is true and false otherwise Read p q as p xor q TruthTable p q p q Where is the difference between or and xor F F Students who have taken calculus or biology can take this class Is tltistq orp q The use of or in English is usually inclusive ie v How can we make this statement exclusive ie gtgt Students who have taken calculus or biology but not both can enroll in this class Note that either or is supposed to be exclusive but we o en 531156 Conditional Statement Truth Table 1 Definition Let p and q be propositions The conditional statement pgtq is false whenp is true and q is false and true otherwise p is called the hypothesis and q the conclusion p only if q many more examples in the boo wemes Had T T Read pgtq as ifp then q p implies q F F k Examples Ifl am elected then I will lower taxes gtgt pgtq with p elected and q taxes p It rains q We get wet gtgt If it rains then we will get wet gtgt We will get wet whenever it rains gtgt It rains only if we get wet CS 2253 Discrete Mathematical Structure 77 Carola Wenc 7 Biconditional Statement lt gt Truth Table Definition Let p and q be propositions The biconditional statement iff pgtq is true q peq when p and q have the same truth value and T T T false otherwise T F F Readplt gtq as p ifand only if q F T F P i q F F T Example You can take the ight if and only if you buy a ticket 827I8 cs 2255 Dtscrete Mathematical Structure W Carola Wenc a

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