Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

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 
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 C

Question 4

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)?

Accepted Answer

A) $(x)[~(Cx · Ex) ? (Bx \vee Rx)]$ 
B) $(x)[(Bx · Rx) ? ~(Cx \vee Ex)]$ 
C) $(?x)[(Bx · Rx) \vee ~(Cx\vee Ex)]$ 
D) $(?x)[(Bx · Rx) · ~(Cx \vee Ex)]$ 
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 5

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

Accepted Answer

A) All 
B) Some 
C) Wild 
A) All 
B) Some 
C) Wild

Question 6

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

Accepted Answer

A) True 
 B)False

Question 7

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.

Accepted Answer

A) True 
 B)False

Question 8

Which statement is true of asyllogistic arguments?

Accepted Answer

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. 
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.

Question 9

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

Accepted Answer

A) $(x)[(Rx · Ax) ? (Cx\vee Dx)]$ 
B) $(x)[(Rx · Ax) ? (Cx · Dx)]$ 
C) $(x)[(Cx · Dx) ? (Rx · Ax)]$ 
D) $(x)[(Rx · Ax) ? (Cx ?Dx)]$ 
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 10

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.)

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

A) universalization 
B) generalization 
C) Simplification 
A) universalization 
B) generalization 
C) Simplification

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

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

Accepted Answer

A) negation 
B) predication 
C) quantification 
A) negation 
B) predication 
C) quantification

Question 15

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.

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

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. 
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 17

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

Accepted Answer

A) negation 
B) predication 
C) instantiatio 
A) negation 
B) predication 
C) instantiatio

Question 18

"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?

Accepted Answer

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. 
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 19

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

Accepted Answer

A) True 
 B)False

Question 20

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

Accepted Answer

A) person 
B) variable 
C) constant 
A) person 
B) variable 
C) constant

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

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

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

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)?

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

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

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.

Which statement is true of asyllogistic arguments?

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

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.)

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

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

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

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

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.

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

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

"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?

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

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

Basic Logical Concepts

Analyzing Arguments

Language and Definitions

Fallacies

Categorical Propositions

Categorical Syllogisms

Syllogisms in Ordinary Language

Propositional Logic I

Propositional Logic II

Analogical Reasoning

Causal Reasoning

Science and Hypothesis

Probability

Filters

Exam 10: Predicate Logic

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

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

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

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)?

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

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

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.

Which statement is true of asyllogistic arguments?

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

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.)

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

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

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

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

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.

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

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

"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?

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

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

Basic Logical Concepts

Analyzing Arguments

Language and Definitions

Fallacies

Categorical Propositions

Categorical Syllogisms

Syllogisms in Ordinary Language

Propositional Logic I

Propositional Logic II

Analogical Reasoning

Causal Reasoning

Science and Hypothesis

Probability

Filters

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