Question 1

Identify the type of statement represented by the following. (x)Ex

Accepted Answer

A) open sentence 
B) singular 
C) quantified existential 
D) quantified universal 
E) None of these answers are correct. 
A) open sentence 
B) singular 
C) quantified existential 
D) quantified universal 
E) None of these answers are correct.

Question 2

Identify the type of statement represented by the following. MA

Accepted Answer

A) open sentence 
B) singular 
C) quantified existential 
D) quantified universal 
E) None of these answers are correct. 
A) open sentence 
B) singular 
C) quantified existential 
D) quantified universal 
E) None of these answers are correct.

Question 3

Identify the quantity and quality of the following statement. (x)(Fx $\supset$ Gx)

Accepted Answer

A) quantity: universal; quality: affirmative 
B) quantity: universal; quality: negative 
C) quantity: particular; quality: affirmative 
D) quantity: particular; quality: negative 
E) None of these answers are correct. 
A) quantity: universal; quality: affirmative 
B) quantity: universal; quality: negative 
C) quantity: particular; quality: affirmative 
D) quantity: particular; quality: negative 
E) None of these answers are correct.

Question 4

The statement [(x)Fx $\supset$ (x)Gx] $\supset$ (y)[($\exists$z)Mz • Ly] is which kind of statement?

Accepted Answer

A) atomic singular statement 
B) truth-functional compound of singular atomic statements 
C) quantifier applied to atomic open sentence 
D) truth-functional compound of open sentences within the scope of a quantifier 
E) truth-functional compound of quantified statements 
A) atomic singular statement 
B) truth-functional compound of singular atomic statements 
C) quantifier applied to atomic open sentence 
D) truth-functional compound of open sentences within the scope of a quantifier 
E) truth-functional compound of quantified statements

Question 5

The statement (x)[(Sx • Fx) $\bigvee$ (Yx • Tx)] is which kind of statement?

Accepted Answer

A) atomic singular statement 
B) truth-functional compound of singular atomic statements 
C) quantifier applied to atomic open sentence 
D) truth-functional compound of open sentences within the scope of a quantifier 
E) truth-functional compound of quantified statements 
A) atomic singular statement 
B) truth-functional compound of singular atomic statements 
C) quantifier applied to atomic open sentence 
D) truth-functional compound of open sentences within the scope of a quantifier 
E) truth-functional compound of quantified statements

Question 6

Which of the following is the universal instantiation rule?

Accepted Answer

A) (x)( ...x ...).Therefore, ( ...a ...) 
B) ~(x)( ...x ...).Therefore, ($\exists$x)~( ...x ...) 
C) ( ...a ...).Therefore, ($\exists$x)( ...x ...) 
D) ($\exists$x)( ...x ...).Therefore, ( ...a ...) 
E) ( ...a ...).Therefore, (x)( ...x ...) 
A) (x)( ...x ...).Therefore, ( ...a ...) 
B) ~(x)( ...x ...).Therefore, ($\exists$x)~( ...x ...) 
C) ( ...a ...).Therefore, ($\exists$x)( ...x ...) 
D) ($\exists$x)( ...x ...).Therefore, ( ...a ...) 
E) ( ...a ...).Therefore, (x)( ...x ...)

Question 7

Identify the quantity and quality of the following statement form. Some shopping carts have squeaky wheels.

Accepted Answer

A) quantity: universal; quality: affirmative 
B) quantity: universal; quality: negative 
C) quantity: particular; quality: affirmative 
D) quantity: particular; quality: negative 
E) None of these answers are correct. 
A) quantity: universal; quality: affirmative 
B) quantity: universal; quality: negative 
C) quantity: particular; quality: affirmative 
D) quantity: particular; quality: negative 
E) None of these answers are correct.

Question 8

Symbolize the following statement. All seniors who have fulfilled the requirements will graduate in May.

Accepted Answer

A) (x)[(Sx • Fx) $\supset$ Gx] 
B) (x)[Sx • Fx) $\supset$ ~Gx] 
C) ($\exists$x)[(Sx • Fx) • Gx] 
D) ($\exists$x)[(Sx • Fx) • ~Gx] 
E) None of these answers are correct. 
A) (x)[(Sx • Fx) $\supset$ Gx] 
B) (x)[Sx • Fx) $\supset$ ~Gx] 
C) ($\exists$x)[(Sx • Fx) • Gx] 
D) ($\exists$x)[(Sx • Fx) • ~Gx] 
E) None of these answers are correct.

Question 9

In the following proof, which justification is correct for line 3? $\begin{array}{llcc}
  \text { (1) $ \sim \mathrm{Da} $ } &&\text {  Premise}   \
 \text {  (2) $ (x)(\sim \mathrm{C} x \supset \mathrm{D} x) $} & \text {  $/ \mathrm{Ca}$}& \text { Premise/Conclusion } \
 \text { (3) $ \sim \mathrm{Cb} \supset \mathrm{Db} $ } &\
\end{array}$

Accepted Answer

A) 1 Add 
B) 2 UI 
C) Assumption 
D) 1, 2 MT 
E) None of these answers are correct. 
A) 1 Add 
B) 2 UI 
C) Assumption 
D) 1, 2 MT 
E) None of these answers are correct.

Question 10

Symbolize the following statement. Some inventors do not file patent applications.

Accepted Answer

A) (x)(Ix $\supset$Fx) 
B) (x)(Ix $\supset$ ~Fx) 
C) ($\exists$x)(Ix • Fx) 
D) ($\exists$x)(Ix • ~Fx) 
E) None of these answers are correct. 
A) (x)(Ix $\supset$Fx) 
B) (x)(Ix $\supset$ ~Fx) 
C) ($\exists$x)(Ix • Fx) 
D) ($\exists$x)(Ix • ~Fx) 
E) None of these answers are correct.

Question 11

Symbolize the following statement form. Some A are B.

Accepted Answer

A) (x)(Ax $\supset$Bx) 
B) (x)(Ax $\supset$ ~Bx) 
C) ($\exists$x)(Ax • Bx) 
D) ($\exists$x)(Ax • ~Bx) 
E) None of these answers are correct. 
A) (x)(Ax $\supset$Bx) 
B) (x)(Ax $\supset$ ~Bx) 
C) ($\exists$x)(Ax • Bx) 
D) ($\exists$x)(Ax • ~Bx) 
E) None of these answers are correct.

Question 12

Nz is called a(n) _____ sentence and the variable z is said to be _____.

Accepted Answer

A) open; free 
B) closed; bound 
C) open; bound 
D) closed; free 
E) None of these answers are correct. 
A) open; free 
B) closed; bound 
C) open; bound 
D) closed; free 
E) None of these answers are correct.

Question 13

Symbolize the following statement form. No A are B.

Accepted Answer

A) (x)(Ax $\supset$ Bx) 
B) (x)(Ax $\supset$ ~Bx) 
C) ($\exists$x)(Ax • Bx) 
D) ($\exists$x)(Ax • ~Bx) 
E) None of these answers are correct. 
A) (x)(Ax $\supset$ Bx) 
B) (x)(Ax $\supset$ ~Bx) 
C) ($\exists$x)(Ax • Bx) 
D) ($\exists$x)(Ax • ~Bx) 
E) None of these answers are correct.

Question 14

Which of the following is the existential generalization rule?

Accepted Answer

A) (x)( ...x ...).Therefore, ( ...a ...) 
B) ~(x)( ...x ...).Therefore, ($\exists$x)~( ...x ...) 
C) ( ...a ...).Therefore, ($\exists$x)( ...x ...) 
D) ($\exists$x)( ...x ...).Therefore, ( ...a ...) 
E) ( ...a ...).Therefore, (x)( ...x ...) 
A) (x)( ...x ...).Therefore, ( ...a ...) 
B) ~(x)( ...x ...).Therefore, ($\exists$x)~( ...x ...) 
C) ( ...a ...).Therefore, ($\exists$x)( ...x ...) 
D) ($\exists$x)( ...x ...).Therefore, ( ...a ...) 
E) ( ...a ...).Therefore, (x)( ...x ...)

Question 15

In the following proof, which justification is correct for line 3? $\begin{array}{llcc}
  \text { (1) $ \sim \mathrm{Ba} $ } & & \text {  Premise}  \
 \text { (2) $ (x)(\mathrm{C} x \vee \mathrm{B} x) $ }&/ \mathrm{Ca} &  \text {Premise/Conclusion  }\
 \text{ (3) $ \mathrm{Ca} \vee \mathrm{Ba} $ }&\
\end{array}$

Accepted Answer

A) 1 Add 
B) 2 Simp 
C) 1, 3 DS 
D) 2 UI 
E) None of these answers are correct. 
A) 1 Add 
B) 2 Simp 
C) 1, 3 DS 
D) 2 UI 
E) None of these answers are correct.

Question 16

Symbolize the following statement. No modern physicists use epicycles to explain the motion of the planets.

Accepted Answer

A) (x)(Mx $\supset$ Ex) 
B) (x)(Mx $\supset$ ~Ex) 
C) ($\exists$x)(Mx • Ex) 
D) ($\exists$x)(Mx • ~Ex) 
E) None of these answers are correct. 
A) (x)(Mx $\supset$ Ex) 
B) (x)(Mx $\supset$ ~Ex) 
C) ($\exists$x)(Mx • Ex) 
D) ($\exists$x)(Mx • ~Ex) 
E) None of these answers are correct.

Question 17

Symbolize the following statement. No astronomers believe in astrology.

Accepted Answer

A) (x)(Ax $\supset$ Bx) 
B) (x)(Ax $\supset$ ~Bx) 
C) ($\exists$x)(Ax • Bx) 
D) ($\exists$x)(Ax • ~Bx) 
E) None of these answers are correct. 
A) (x)(Ax $\supset$ Bx) 
B) (x)(Ax $\supset$ ~Bx) 
C) ($\exists$x)(Ax • Bx) 
D) ($\exists$x)(Ax • ~Bx) 
E) None of these answers are correct.

Question 18

Symbolize the following statement. A few English monarchs were not completely sane.

Accepted Answer

A) (x)(Mx $\supset$ Sx) 
B) (x)(Mx $\supset$ ~Sx) 
C) ($\exists$x)(Mx • Sx) 
D) ($\exists$x)(Mx • ~Sx) 
E) None of these answers are correct. 
A) (x)(Mx $\supset$ Sx) 
B) (x)(Mx $\supset$ ~Sx) 
C) ($\exists$x)(Mx • Sx) 
D) ($\exists$x)(Mx • ~Sx) 
E) None of these answers are correct.

Question 19

Translate the following symbolized categorical statement into English using the provided key. $ \mathrm{L} x=x $ is limestone$\quad $$\quad $$\quad $$\quad $$\quad $$ \mathrm{M} x=x $ is metamorphic
$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$(x)(\mathrm{L} x \Rightarrow?\mathrm{M} x)$

Accepted Answer

A) All limestone is metamorphic. 
B) No limestone is metamorphic. 
C) Some limestone is metamorphic. 
D) Some limestone is not metamorphic. 
E) None of these answers are correct. 
A) All limestone is metamorphic. 
B) No limestone is metamorphic. 
C) Some limestone is metamorphic. 
D) Some limestone is not metamorphic. 
E) None of these answers are correct.

Question 20

Symbolize the following statement. All rocks break windows.

Accepted Answer

A) (x)(Rx $\supset$ Bx) 
B) (x)(Rx $\supset$ ~Bx) 
C) ($\exists$x)(Rx • Bx) 
D) ($\exists$x)(Rx • ~Bx) 
E) None of these answers are correct. 
A) (x)(Rx $\supset$ Bx) 
B) (x)(Rx $\supset$ ~Bx) 
C) ($\exists$x)(Rx • Bx) 
D) ($\exists$x)(Rx • ~Bx) 
E) None of these answers are correct.

Identify the type of statement represented by the following. (x)Ex

Identify the type of statement represented by the following. MA

Identify the quantity and quality of the following statement. (x)(Fx $\supset$ Gx)

The statement [(x)Fx $\supset$ (x)Gx] $\supset$ (y)[( $\exists$ z)Mz • Ly] is which kind of statement?

The statement (x)[(Sx • Fx) $\bigvee$ (Yx • Tx)] is which kind of statement?

Which of the following is the universal instantiation rule?

Identify the quantity and quality of the following statement form. Some shopping carts have squeaky wheels.

Symbolize the following statement. All seniors who have fulfilled the requirements will graduate in May.

Symbolize the following statement. Some inventors do not file patent applications.

Symbolize the following statement form. Some A are B.

Nz is called a(n) _ sentence and the variable z is said to be _.

Symbolize the following statement form. No A are B.

Which of the following is the existential generalization rule?

Symbolize the following statement. No modern physicists use epicycles to explain the motion of the planets.

Symbolize the following statement. No astronomers believe in astrology.

Symbolize the following statement. A few English monarchs were not completely sane.

Translate the following symbolized categorical statement into English using the provided key. $\mathrm{L} x=x$ is limestone $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\mathrm{M} x=x$ is metamorphic $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $(x)(\mathrm{L} x \Rightarrow?\mathrm{M} x)$

Symbolize the following statement. All rocks break windows.

Classification

Definitions

Propositions

Argument Analysis

Fallacies

Categorical Propositions

Categorical Syllogisms

Reasoning With Syllogisms

Propositional Logic-Propositions

Propositional Logic-Arguments

Inductive Generalizations

Argument by Analogy

Statistical Reasoning

Explanation

Probability

Filters

Exam 11: Predicate Logic

Identify the type of statement represented by the following. (x)Ex

Identify the type of statement represented by the following. MA

Identify the quantity and quality of the following statement. (x)(Fx ⊃\supset⊃ Gx)

The statement [(x)Fx ⊃\supset⊃ (x)Gx] ⊃\supset⊃ (y)[( ∃\exists∃ z)Mz • Ly] is which kind of statement?

The statement (x)[(Sx • Fx) ⋁\bigvee⋁ (Yx • Tx)] is which kind of statement?

Which of the following is the universal instantiation rule?

Identify the quantity and quality of the following statement form. Some shopping carts have squeaky wheels.

Symbolize the following statement. All seniors who have fulfilled the requirements will graduate in May.

Symbolize the following statement. Some inventors do not file patent applications.

Symbolize the following statement form. Some A are B.

Nz is called a(n) _____ sentence and the variable z is said to be _____.

Symbolize the following statement form. No A are B.

Which of the following is the existential generalization rule?

Symbolize the following statement. No modern physicists use epicycles to explain the motion of the planets.

Symbolize the following statement. No astronomers believe in astrology.

Symbolize the following statement. A few English monarchs were not completely sane.

Symbolize the following statement. All rocks break windows.

Classification

Definitions

Propositions

Argument Analysis

Fallacies

Categorical Propositions

Categorical Syllogisms

Reasoning With Syllogisms

Propositional Logic-Propositions

Propositional Logic-Arguments

Inductive Generalizations

Argument by Analogy

Statistical Reasoning

Explanation

Probability

Filters

Identify the quantity and quality of the following statement. (x)(Fx $\supset$ Gx)

The statement [(x)Fx $\supset$ (x)Gx] $\supset$ (y)[( $\exists$ z)Mz • Ly] is which kind of statement?

The statement (x)[(Sx • Fx) $\bigvee$ (Yx • Tx)] is which kind of statement?

Nz is called a(n) _ sentence and the variable z is said to be _.