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Study examples - ∀ x (Dodec(x) → Medium(x)) ∀ x...

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Which of the following formulae are sentences? What kinds of sentences are they? 1. x Cube(x) y Tet(y) 2. y (Tet(y) Dodec(y)) 3. x (Dodec(x) Large(x)) 4. x Smaller(b, x) 5. Medium(z) 6. x Tet(x) Small(x) 7. x (Cube(x) z ¬ Dodec(z)) 8. ¬ x Smaller(b, x) 9. y Medium(y) z Tet(z) 10. x y Likes(x, y) What would be proper translations for the following sentences? 1. x (Tet(x) Small(x)) 2. ¬ x (Tet(x) Small(x)) 3. x ¬ (Tet(x) Small(x)) 4. x (Tet(x) ¬ Small(x)) 5. x (Large(x) Cube(x)) 6. ¬ x (Large(x) Cube(x)) 7. x ¬ (Large(x) Cube(x)) 8. x ( ¬ Large(x) Cube(x)) 9. x y Likes(x, y) 10. y x Likes(x, y) What would be a counterexample for the following invalid argument?
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Unformatted text preview: ∀ x (Dodec(x) → Medium(x)) ∀ x (Medium(x) → LeftOf(x, a)) So, ∃ x (Dodec(x) ∧ LeftOf(x, a)) Consider the following premises (from Lewis Carroll). What conclusion(s) can be drawn from them? (1) Babies are illogical. (2) Nobody is despised who can manage a crocodile. (3) Illogical persons are despised. Predicate symbols needed: Baby(x), [ “x is a baby.” ] Logical(x) [ “x is logical.” ] CanManageCrocodile(x) [ “x can manage a crocodile.” ] Despised(x) [ “x is despised.” ] Translations: (1) (2) (3) Proof for ∀ x (Baby(x) → ¬ CanManageCrocodile(x)) or, “No baby can manage a crocodile.”...
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This note was uploaded on 06/07/2011 for the course PHIL 110 taught by Professor ? during the Fall '06 term at South Carolina.

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Study examples - ∀ x (Dodec(x) → Medium(x)) ∀ x...

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