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0123-extra - CPSC 121 Lecture 9 Supplementary Examples Here...

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Unformatted text preview: CPSC 121 Lecture 9 Supplementary Examples January 23, 2009 Here are supplementary notes to provide additional examples, some of which also may be presented in class (or tutorial). Examples inspired by Lewis Carroll’s Alice in Wonderland Example 1: “If Alice eats food then she grows or shrinks.” ( D = set of all food). Let E ( x ) : Alice eats food x S ( x ) : food x makes Alice shrink G ( x ) : food x makes Alice grow Translation: ∀ x,E ( x ) → ( S ( x ) ∨ G ( x )) Example 2: Let F ( x ) : x is a fierce creature L ( x ) : x is a lion C ( x ) : x drinks coffee ( D = set of all creatures) Translate: “Some lions do not drink coffee.” Translation: ∃ x, ( L ( x ) ∧ C ( x )) Translate: “All lions are fierce.” Translation: ∀ x, ( L ( x ) → F ( x )) Translate: “All fierce creatures are not lions.” NOTE: We claim there are two interpretations. Translation 1: ∀ x, ( F ( x ) → L ( x )) Interpretation 1: “Nothing that is fierce is a lion.” Translation 2: ∃ x, ( F ( x ) ∧ L ( x )) Interpretation 2: “There is some creature that is fierce but not a lion.” Let’s look at Translation 2 more closely: ∃ x, ( F ( x ) ∧ L ( x )) ≡ ∃ x, F ( x ) → L ( x ) by p → q ≡ p ∧ q ≡ ∀ x,F ( x ) → L ( x ) by generalized De Morgan Thus, the ambiguity arises from whether the negation applies to...
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This note was uploaded on 01/09/2010 for the course CPSC 121 taught by Professor Belleville during the Spring '08 term at UBC.

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0123-extra - CPSC 121 Lecture 9 Supplementary Examples Here...

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