Deck 10: Predicate Logic

Question 1

"The only people who cannot vote are those convicted of a felony." Translated into symbols, this would be:

A)(x)(Fx ? ~V x) · (x)(~Fx ? V x)
B)(x)(Fx ? Vx)
C)(x)(~Fx ? Vx)
D)(x)(Fx ? ~Vx)

Answer 1

(x)(Fx ? ~V x) · (x)(~Fx ? V x)

Question 2

Which of the assignments of truth values for Na, Ra, and Va shows the following proof invalid?
1)(x)(Nx ? Rx) $\quad$ Na ? Ra
2.(x)(Vx ? Nx) $\quad$ Va ? Na
3.? (x)(Rx ? Vx) $\quad$ Ra ? Va

A)Na Ra Va - TTF
B)Na Ra Va - TFT
C)Na Ra Va - FFT
D)Na Ra Va - FTT

Answer 2

Na Ra Va - TTF

Question 3

Which statement is true of asyllogistic arguments?

A)They are arguments using propositional variables and quantifiers.
B)They can be translated with the help of quantifiers and propositional functions into forms compatible with Aristotelian syllogisms.
C)They are called asyllogistic because they are not actual arguments.
D)They are cogent arguments that cannot be reduced to standard-form categori- cal syllogisms.

Answer 3

They are cogent arguments that cannot be reduced to standard-form categori- cal syllogisms.

Question 4

Which of the choices below is a correct translation of "Real apricots are crunchy and delicious" (R, A, C, D)?

A) $(x)[(Rx · Ax) ? (Cx\vee Dx)]$
B) $(x)[(Rx · Ax) ? (Cx · Dx)]$
C) $(x)[(Cx · Dx) ? (Rx · Ax)]$
D) $(x)[(Rx · Ax) ? (Cx ?Dx)]$

Question 5

Which of the choices below is a correct translation of "Rocks will fall if and only if they are nudged" (R, F, N)

A)(x)[Rx ? (Fx ? Nx)]
B)(x)[(Fx ? Nx) ? Rx]
C)(x)[(Rx ? Nx) ? Fx]
D)(x)[(Rx ? (Nx ? Fx)]

Question 6

Which of the following is a correct translation of "Not all books that are easy to read are either cheap or enjoyable" (B, R, C, E)?

A) $(x)[~(Cx · Ex) ? (Bx \vee Rx)]$
B) $(x)[(Bx · Rx) ? ~(Cx \vee Ex)]$
C) $(?x)[(Bx · Rx) \vee ~(Cx\vee Ex)]$
D) $(?x)[(Bx · Rx) · ~(Cx \vee Ex)]$

Question 7

Where is the mistake in the following proof?
1)(?x)(Fx · Ax)
2.(?x)(Fx · Ox)
3.? (?x)(Ax · Ox)
4.Fb · Ab (1, E.I.)
5.Fb · Ob (2, E.I.)
6.Ab · Fb (4, Com.)
7.Ab (6, Simp.)
8.Ob · Fb (5, Com.)
9.Ob (8, Simp.)
10.Ab · Ob (7, 9, Conj.)
11.(?x)(Ax · Ox) (10, E.G.)

A)line 4
B)line 8
C)line 5
D)line 9

Question 8

"Hotels are both expensive and depressing.Some hotels are shabby.Therefore, some expensive things are shabby." Quantifier logic is superior to syllogistic logic in rendering arguments such as this one into symbolic form.Why?

A)Quantifier logic allows us to take arguments at face value; it is a lot of unnecessary trouble to rearrange them into syllogisms and a lot easier to have a logic that is a better match for ordinary language.
B)Syllogistic logic fell in after the discovery of the existential fallacy.The new logic allows us to remove ourselves from the problem using quantifiers.
C)Syllogistic logic was burdened with meaningless and redundant structure such as the meticulous stacking of major and minor premises into the correct order.
D)Quantifier logic allows us to "bundle" concepts with parentheses instead of "hiding" them in the subject or predicate terms, where they become unavailable for use in the proof.

Question 9

The principle of Universal Instantiation (U.I.) asserts that:

A)from the substitution instance of a particular propositional function with respect to the name of any arbitrarily selected individual one can validly infer the universal quantification of that propositional function.
B)from any true substitution instance of a propositional function we may validly infer the universal instantiation of that propositional function.
C)any substitution instance of a propositional function can be validly inferred from its existential quantification.
D)any substitution instance of a propositional function can be validly inferred from its universal quantification.

Question 10

Why do we use Universal Generalization (U.G.) in proofs?

A)to allow us to reason about the characteristics of individuals from premises that include generalizations
B)to allow us to unlock simple statements from inside of compound statements about particular individuals so that they may be used in proofs
C)to take isolated instances and put them in the form of "all" statements so that conclusions may be drawn from them about more than one individual
D)to get from compound statements to simple ones so we can use the compo- nents of those statements

Question 11

The existential quantifier (?x) stands for x or the phrase "there is at least one
x such that."

Question 12

The biconditional relationship [(?x)Nx] ? [~(x)~Nx] tells us that the universal and
existential quantifiers negate each other, and so the two quantifiers may never be
transformed into one another.

Question 13

The universal quantifier may be dropped from a statement in a proof because of the
principle that any substitution instance whatsoever may be validly inferred from a
universally quantified proposition.

Question 14

The rule of Existential Generalization (E.G.) is used to justify this inference:
(x)(Px ? Qx)
? Pa ? Qa

Question 15

To prove invalidity when working with quantified propositions, first construct a
possible universe containing two members.

Question 16

Matching:

-In quantifier logic, the lower-case c (denoting, say, Carl) is an individual ________.

A)person
B)variable
C)constant

Question 17

Matching:

-The process of placing a universal quantifier before a propositional function is called

A)universalization
B)generalization
C)Simplification

Question 18

Matching:

-" professors are not human" may be rendered in symbolic logic as (?x)(Px · ~Hx).

A)All
B)Some
C)Wild

Question 19

Matching:

-Any formula in which ________ signs apply only to simple predicates is called a normalform formula.

A)negation
B)predication
C)quantification

Question 20

Matching:

-In quantification theory, propositions are formed either by quantification oby

A)negation
B)predication
C)instantiatio