CSE 321 -- HANDOUT ON PRACTICING NESTED QUANTIFERS. WINTER 2010 For problems 1-5, assume that the following predicates are defined: Student(x) means that x is a student Advisor(x, y) means that x is an advisor of y Translate the following sentences into predicate logic using quantifiers when appropriate assuming that the domain is the set of all students and faculty at the University of Washington and assuming that a person is an advisor if and only if they advise someone. 1. Every student has an advisor 2. Everyone with an an advisor is a student 3. Everyone is either a student or an advisor or both. 4. Every student has exactly one advisor 5. Only students have advisors For problems 6-10, assume that the following predicates are defined: Cool(x) means that x is cool Proof(x) means that x is a proof Wears(x, y) means that x wears y Translate the following sentences into predicate logic using quantifiers when appropriate. 6. All the stuff worn by cool people is cool. 7. You can wear all cool stuff and still not be cool. 8. Proofs are cool. 9. You will not be cool if you wear a proof. 10. Translate the following logical expression into English: exists x.(Cool(x) and forall y. Wears(y, x)) For problems 11-15, assume that the following predicates are defined: Rich(x) means that x is rich RockStar(x) means that x is a rock star Fan(x, y) means that x is a fan of y Translate the following sentences into predicate logic using quantifiers when appropriate. 11. Every rock star has fans. 12. No rock star has everyone as a fan. 13. You can't be a rock star if you're not rich. 14. Some rich people aren't rock stars. 15. Translate the following logical expression into English: not exists x. forall y (RockStar(y) --> Fan(x, y)) For problesm 16-20, assume that the following predicates are defined: Likes(drinker, beer) Frequents(drinker, bar) Serves(bar, beer) Express the following sentences in First Order Logic using quantifiers: 16. Every drinker likes 'Bud' 17. Some drinker likes only 'Bud' 18. Every drinker frequents some bar that serves 'Bud' 19. Every drinker frequents some bar that serves some beer that they don't like 20. Some drinker frequents only bars that seve only beer that that they don't like