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ICS253_Lecture_08

# ICS253_Lecture_08 - Outline Translating Mathematical...

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Outline Translating Mathematical Statements into Statements Involving Nested Quantifiers Translating from Nested Quantifiers into English Translating English Sentences into Logical Expression Negating Nested Quantifiers ICS 253 Lecture 08 Dr. Adel F. Ahmed ICS - CCSE - KFUPM October 27, 2008 Dr. Adel F. Ahmed ICS 253 Lecture 08

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Outline Translating Mathematical Statements into Statements Involving Nested Quantifiers Translating from Nested Quantifiers into English Translating English Sentences into Logical Expression Negating Nested Quantifiers Translating Mathematical Statements into Statements Involving Nested Quantifiers The sum of two positive integers . . . Example: Every real number except zero has . . . Example Expressing lim x a f ( x ) = L Translating from Nested Quantifiers into English Example: x ( C ( x ) ∨ ∃ y ( C ( y ) F ( x , y ))) Example: x y z (( F ( x , y ) F ( x , z ) y 6 = z )) → ¬ F ( y , z ) Translating English Sentences into Logical Expression Example: If a person is a female and . . . Example: Everyone has exactly one best friend Example: There is a woman who has taken . . . Negating Nested Quantifiers Example: ¬∀ x y ( xy = 1) Example: There does not exist a woman who . . . Example: lim x a f ( x ) does not exist Dr. Adel F. Ahmed ICS 253 Lecture 08
Outline Translating Mathematical Statements into Statements Involving Nested Quantifiers Translating from Nested Quantifiers into English Translating English Sentences into Logical Expression Negating Nested Quantifiers The sum of two positive integers . . . Example: Every real number except zero has . . . Example Expressing lim x a f ( x ) = L Translating Mathematical Statements into Statements Involving Nested Quantifiers I Some examples are presented to illustrate the techniques and skills of translating Mathematical Statements into Statements Involving Nested Quantifiers Dr. Adel F. Ahmed ICS 253 Lecture 08

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Outline Translating Mathematical Statements into Statements Involving Nested Quantifiers Translating from Nested Quantifiers into English Translating English Sentences into Logical Expression Negating Nested Quantifiers The sum of two positive integers . . . Example: Every real number except zero has . . . Example Expressing lim x a f ( x ) = L Example: The sum of two positive integers . . . Example: Translate the statement “ The sum of two positive integers is always positive ” into logical expression Dr. Adel F. Ahmed ICS 253 Lecture 08
Outline Translating Mathematical Statements into Statements Involving Nested Quantifiers Translating from Nested Quantifiers into English Translating English Sentences into Logical Expression Negating Nested Quantifiers The sum of two positive integers . . . Example: Every real number except zero has . . . Example Expressing lim x a f ( x ) = L Example: The sum of two positive integers . . .

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ICS253_Lecture_08 - Outline Translating Mathematical...

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