2000-final
Formal Logic I: Final Exam
Kelli Potter
Utah Valley University
I. Translations into QL. Translate the following sentences into the language of QL. Indicate what
the predicates (1-place, 2-place, etc.) and names (/individual constants) mean.
1. Not every democrat is a liberal.
2. Alice saw nobody on the road.
3. There are protestors in the streets.
4. If any task remains unfinished, nobody will be able go home.
5. All logicians are smarter than any theologian.
6. Every particle subject to no net force has constant velocity.
7. Logic students may use only the rules on the back page of the book.
8. Some wise people aren’t religious.
II. Translation from QL into English. Translate the following sentences into English. You will
have to determine and indicate what the predicates mean. [Note: I use parentheses as a marker
around the quantifiers to make the structure easier to see. The text doesn’t use them.]
9. (∀x) ¬Gx ⊃ (∃y)Jy
10. (∀x)(∃y)(Lxy)
11. (∃x) ¬Fx ∨ (∃y)Hy
12. (∀x)[Px ⊃ (Qx ⊃ Rx)]
13. (∃x)Ax ⊃ (∀y)(By ⊃ Cy)
14. (∃x)Kx ∨ (∀y)(Ky ⊃ Hy)
15. (∀x)(Tx ⊃ ¬Mx)
II. Checking for validity. Use truth tables or truth trees to determine whether the following
arguments are (tautologically) valid.
16. Q ⊃ (P ⊃ R), P ⊃ Q ∴ ¬P ∨ R
17. ¬P ∨ Q, P ⊃ ¬Q ∴ ¬P
18. ¬Q ∨ (R ∧ S), S ⊃ ¬Q ∴ S
19. P ⊃ (Q ⊃ R), R ⊃ S ∴ ¬(P ∧ ¬S)
IV. Conceptual questions. Write a word, sentence, or short paragraph answering the following
questions.
20. Explain why PL is truth-functional and QL is not.
21. Explain the difference between a name and a variable in QL.
22. How did Frege use the concept of a function to incorporate quantifiers into logic?
23. Explain the meaning of the universal quantifier.
24. Is it possible to eliminate one of the quantifiers and have QL still be complete?
Explain your answer.
25. [Bonus question] If we assume that the domain has three members, which are
named ‘a’, ‘b’, and ‘c’, then (∀x)Px is equivalent to what QL sentence using only
predicates, names, and logical operators (no quantifiers)?