Unformatted text preview: ∀ x ( D ( x ) → F ( x )). The negation is ¬∀ x ( D ( x ) → F ( x )) ≡ ∃ x ¬ ( D ( x ) → F ( x )) ≡ ( ∃ x ( D ( x ) ∧ ¬ F ( x ). Of course, there are several other things this is equivalent to. The translation of this negation is “There exists a dog that does not have ²eas.” b) There exists a pig that can swim and catch ±sh. Let P ( x ) mean “ x is a pig”, S ( x ) mean “ x can swim”, and F ( x ) mean “ x can ±sh”. Then we write this as ∃ x ( P ( x ) ∧ S ( x ) ∧ F ( x )). The negation is ¬∃ x ( P ( x ) ∧ S ( x ) ∧ F ( x )) ≡ ∀ x ¬ ( P ( x ) ∧ S ( x ) ∧ F ( x )). Again, there are numerous things this is equivalent to. One translation of this is “No pig can swim and ±sh”. 1...
View
Full
Document
This note was uploaded on 08/11/2008 for the course MATH 240 taught by Professor Miller during the Fall '08 term at University of Wisconsin.
 Fall '08
 Miller
 Math, Logic

Click to edit the document details