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Study examples

# Study examples - Which of the following formulae are...

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Which of the following formulae are sentences? What kinds of sentences are they? 1. x Cube(x) y Tet(y) [WFF; Sentence: Conjunction] 2. y (Tet(y) Dodec(y)) [WFF; Sentence: Universal] 3. x (Dodec(x) Large(x)) [WFF; Sentence: Universal] 4. x Smaller(b, x) [WFF; Sentence: Existential] 5. Medium(z) [WFF; Not a sentence] 6. x Tet(x) Small(x) [WFF; Not a sentence] 7. x (Cube(x) z ¬ Dodec(z)) [WFF; Sentence: Universal] 8. ¬ x Smaller(b, x) [WFF; Sentence: Negation] 9. y Medium(y) z Tet(z) [WFF; Sentence: Conditional] 10. x y Likes(x, y) [WFF; Sentence: Universal] **Only numbers 2, 3, 4, 7, and 10 are quantificational sentences. What would be proper translations for the following sentences? 1. x (Tet(x) Small(x)) “All tetrahedrons are small.” 2. ¬ x (Tet(x) Small(x)) “Not all tetrahedrons are small.” 3. x ¬ (Tet(x) Small(x)) “Everything is a tetrahedron that is not small.” 4. x (Tet(x) ¬ Small(x)) “No tetrahedrons are small.” 5. x (Large(x) Cube(x)) “Something is a large dodecahedron.”

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