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Unformatted text preview: lent” you must give an explanation. (a) ∀ x ( Q ( x ) ∧ P ( x )) and ∀ xQ ( x ) ∧ ∀ xP ( x ) (b) ∀ x ( Q ( x ) ∨ P ( x )) and ∀ xQ ( x ) ∨ ∀ xP ( x ) (c) ∀ x ( Q ( x ) → P ( x )) and ∀ xQ ( x ) → ∀ xP ( x ) 6. 40 pts. Let L ( x, y ) be the predicate for ” x likes to buy y ” and let S ( y ) stand for ” y is on sale”. Formalize: (a) Everybody likes to buy something, but only if it is on sale. (b) There is something everybody likes to buy if it is on sale. (c) If everything is on sale then everybody likes to buy everything. (d) There is somebody who likes to buy everything if it is on sale. 7. 30 pts. Let N be the set of natural numbers and let n  m stand for that n divides m . Formalize: For every n and m there is some g such that g divides n and m, and if q divides n and m, then q divides g....
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 Spring '11
 JeffWong
 Math, Linear Algebra, Algebra

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