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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,...

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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)?
Answered Same Day Jun 26, 2021

Solution

Rajeswari answered on Jun 26 2021
111 Votes
Question 1.
1. Not every democrat is a liberal.
P(x) = x is democrat
Q(x) = x is liberal
(∃x) (P(x) ∩ {Q(x)}’)
2. Alice saw nobody on the road.
P(x) = Alex saw x
Q(x) = x is on the road
(∀x) (P(x))’∩Q(x)}
3. There are protestors in the streets.
P(x) = x is a protesto
Q(x) = x is in street
(∃x) (P(x)∩Q(x))
4. If any task remains unfinished, nobody will be able go home.
P(x) = x is not finished
Q(y) = nobody can go home
(x,y) {P(x)∩Q(y)}
5. All logicians are smarter than any theologian.
P(x) = x is a logician
Q(x) = x is a theologian
R(x) = x is smarte
(∀x) (P(x)∩Q(x) R(x))
6. Every particle subject to no net force has constant velocity.
P(x) = x is subject to net force
Q(x) = x has constant velocity
(∀x) (P(x)) {Q(x)}’
7. Logic students may use only the rules on the back page of the book.
P(x) = x is logic student
Q(x) = x uses only the rules on the back page of the book
(∃x) (P(x)Q(x))
8. . Some wise people aren’t religious.
P(x) = people are wise
Q(x) = people are religious
(∃x) (P(x)∩Q(x)’)
9. (∀x) ¬Gx ⊃ (∃y)Jy
For all x, if G(x) is not true, then there are y’s for which J(y) is true.
Or if J(y) is true...
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