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# lecture3 - Discrete Computation Structures CSE 2353 Bhanu...

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Discrete Computation Structures CSE 2353 Bhanu Kapoor, PhD Department of Computer Science & Engineering Southern Methodist University, Dallas, TX [email protected] , 214-336-4973 September 03, 2009 Embrey 129, SMU, Dallas, Texas Lecture 03 1

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Lecture 03 Agenda ± Mathematical Logic: Statements ± Logical connectives to combine statements xplore how to draw logical conclusions ± Explore how to draw logical conclusions ± Introduction to Algorithms ± Recap Sets for Quiz ± Quiz # 1 2
Mathematical Logic ± Definition: Methods of reasoning, provides rules and techniques to determine whether an argument is valid ± Theorem: a statement that can be shown to be true (under certain conditions) ² Example: If x is an even integer, then x + 1 is an odd integer ± This statement is true under the condition that x is an integer is ue true 3

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Mathematical Logic ± A statement , or a proposition , is a declarative sentence that is either true or false, but not both ± Lowercase letters denote propositions ² Examples: ± p: 2 is an even number (true) ± q: 3 is an odd number (true) ± r: A is a consonant (false) ² The following are not propositions: ± p: My cat is beautiful : Are you in charge? ± q: Are you in charge? 4
Mathematical Logic ± Truth value ² One of the values “ truth” or “ falsity” assigned to a tatement statement ² True is abbreviated to T or 1 ² False is abbreviated to F or 0 ± Negation ² The negation of p , written ׽ p , is the statement obtained by negating statement p ruth values of nd re opposite ± Truth values of p and ׽ p are opposite ± Symbol ~ is called “ not” ~ p is read as as “not p” ± Example: ² p: A is a consonant p ² ~p: it is the case that A is not a consonant ± q: Are you in charge? 5

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Mathematical Logic ± Truth Table for negation onjunction ± Conjunction ² Let p and q be statements.The conjunction of p and q, written p ר q , is the statement formed by joining statements p and q using the word “and” ² The statement p ר q is true if both p and q are true; therwise false otherwise p ר q is false 6
Mathematical Logic ± Conjunction j ² Truth Table for Conjunction: 7

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Mathematical Logic ± Disjunction et p and q be statements The isjunction ² Let p and q be statements. The disjunction of p and q, written p ש q , is the statement formed by joining statements p and q using the word “or” ² The statement p ש q is true if at least one of the statements p and q is true; otherwise p ש q is false ² The symbol ש is read “or” 8
Mathematical Logic isjunction ± Disjunction ² Truth Table for Disjunction: 9

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Mathematical Logic ± Implication ² Let p and q be statements.The statement “if p then q” is called an implication or ondition condition . ² The implication “if p then q” is written p q is read: ² p q is read: ± “If p, then q” ± “p is sufficient for q” ± q if p ± q whenever p 10
Mathematical Logic ± Implication ² Truth Table for Implication: ² p is called the hypothesis, q is called the onclusion conclusion 11

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Mathematical Logic ± Implication ²
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lecture3 - Discrete Computation Structures CSE 2353 Bhanu...

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