Question 1

Symbolize the following statement. At least one U.S.president was a Quaker.

Accepted Answer

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

Question 2

The following inference is an application of which rule? (y)Gy.Therefore, Gb.

Accepted Answer

A) quantifier negation 
B) universal instantiation 
C) existential generalization 
D) existential instantiation 
E) universal generalization 
A) quantifier negation 
B) universal instantiation 
C) existential generalization 
D) existential instantiation 
E) universal generalization

Question 3

The following inference is an application of which rule? ~($\exists$y)~(My • Na).Therefore, (y)(My • Na).

Accepted Answer

A) quantifier negation 
B) universal instantiation 
C) existential generalization 
D) existential instantiation 
E) universal generalization 
A) quantifier negation 
B) universal instantiation 
C) existential generalization 
D) existential instantiation 
E) universal generalization

Question 4

The following inference is an application of which rule? (z)(Az $\supset$Bd).Therefore, Ad $\supset$ Bd.

Accepted Answer

A) quantifier negation 
B) universal instantiation 
C) existential generalization 
D) existential instantiation 
E) universal generalization 
A) quantifier negation 
B) universal instantiation 
C) existential generalization 
D) existential instantiation 
E) universal generalization

Question 5

In the following proof, which justification is correct for line 7? $\begin{array}{llcc}
  \text {(1) $ (x)\{[\mathrm{C} x \cdot(\mathrm{D} x \vee \mathrm{E} x)] \supset \mathrm{F} x\} $  } & & \text {  Premise} \
 \text { (2) $ (\exists y)(E y * \sim \mathrm{Fy}) $ } & \text {$/(\exists x) \sim C x$  }& \text { Premise/Conclusion }\
 \text {(3) $ \mathrm{Ea} * \sim \mathrm{Fa} $  } && \text { 2 EI }\
 \text {  (4) $ [\mathrm{Ca} \cdot(\mathrm{Da} \cup \mathrm{Ea})] D \mathrm{Fa} $} && \text {$ 1 \mathrm{UI} $  }\
 \text {(5) $ -\mathrm{Fa} $  } && \text {$ 3 \mathrm{Simp} $  }\
 \text { (6) $ \sim[\mathrm{Ca} \cdot(\mathrm{Da} \vee \mathrm{Ea})] $ } && \text { $ 4,5 \mathrm{MT} $ }\ 
 \text { (7) $ \sim \mathrm{Ca} v \sim(\mathrm{Da} v \mathrm{Ea})] $ } &\
\end{array}$

Accepted Answer

A) 3 Add 
B) 6 DM 
C) 7 DM 
D) 6 Dist 
E) None of these answers are correct. 
A) 3 Add 
B) 6 DM 
C) 7 DM 
D) 6 Dist 
E) None of these answers are correct.

Question 6

Symbolize the following statement. Only skydivers with much experience perform in thrill shows.

Accepted Answer

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

Question 7

Identify the quantity and quality of the following statement form. Everyone likes to discuss the weather.

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

Which of the following is the existential 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 9

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { C } x = x$ is a crocodile$\quad $$\quad $$\quad $$\quad $$\mathrm { M } x = x$ makes a good pet
$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$( \exists x ) ( \mathrm { C } x \cdot \sim \mathrm { M } x )$

Accepted Answer

A) All crocodiles make good pets. 
B) No crocodiles make good pets. 
C) Some crocodiles make good pets. 
D) Some crocodiles do not make good pets. 
E) None of these answers are correct. 
A) All crocodiles make good pets. 
B) No crocodiles make good pets. 
C) Some crocodiles make good pets. 
D) Some crocodiles do not make good pets. 
E) None of these answers are correct.

Question 10

Symbolize the following statement. All green or yellow vegetables are nutritious.

Accepted Answer

A) (x){[(Gx $\bigvee$ Yx) • Vx] $\supset$ Nx} 
B) (x){[(Gx $\bigvee$ Yx) • Vx] $\supset$~Nx} 
C) ($\exists$x){[(Gx $\bigvee$ Yx) • Vx] • Nx} 
D) ($\exists$x){[(Gx $\bigvee$ Yx) • Vx] • ~Nx} 
E) None of these answers are correct. 
A) (x){[(Gx $\bigvee$ Yx) • Vx] $\supset$ Nx} 
B) (x){[(Gx $\bigvee$ Yx) • Vx] $\supset$~Nx} 
C) ($\exists$x){[(Gx $\bigvee$ Yx) • Vx] • Nx} 
D) ($\exists$x){[(Gx $\bigvee$ Yx) • Vx] • ~Nx} 
E) None of these answers are correct.

Question 11

In the following proof, which justification is correct for line 7? $\begin{array}{llcc}
  \text {(1) $ (x)(\sim \mathrm{N} x \supset \mathrm{B} x) $  } && \text {Premise  }  \
 \text { (2) $ (\exists y) \sim \mathrm{By} $ } & \text {  $I(\exists z)(\mathrm{N} z \quad \vee \sim \mathrm{C} z)$} & \text { Premise/Conclusion } \
 \text {  (3) $ \sim \mathrm{Ba} $} &&2 \mathrm{EI} \
 \text {(4) $ \sim \mathrm{Na} \supset \mathrm{Ba} $  } && 1 \mathrm{UI} \
 \text {(5) $ -\mathrm{Na} 3 $,  } &&4 \mathrm{MI} \
 \text {(6) $ \mathrm{Na} $  } &&5 \mathrm{DN} \
\text { (7) $ \mathrm{Na} v \sim \mathrm{Cba} $ } &\
\end{array}$

Accepted Answer

A) 4 Imp 
B) 6 Add 
C) 6 Taut 
D) Assumption 
E) None of these answers are correct. 
A) 4 Imp 
B) 6 Add 
C) 6 Taut 
D) Assumption 
E) None of these answers are correct.

Question 12

In the following proof, which justification is correct for line 5? $\begin{array}{llcc}
  \text {(1) $ (y)(\mathrm{G} y \supset \mathrm{Hy}) $  } &&\text { Premise }   \
 \text { (2) $ \sim[(\exists z) \mathrm{Hz} \vee(\exists z) \mathrm{I}] $ } &\text {$/ \sim(\exists x) \mathrm{G} x$  } &\text {Premise/Conclusion  } \
 \text { (3) $ (\exists x) \mathrm{G} x $ } &&\text {Assumption  } \
 \text { (4) $ \mathrm{Ga} $ } &&\text { $ 3 \mathrm{EI} $ } \
 \text {  (5) $ \mathrm{Ga} \supset \mathrm{Ha} $} &\
\end{array}$

Accepted Answer

A) Assumption 
B) 3 EI 
C) 1 UI 
D) 4 Add 
E) None of these answers are correct. 
A) Assumption 
B) 3 EI 
C) 1 UI 
D) 4 Add 
E) None of these answers are correct.

Question 13

Symbolize the following statement. The painting is beautiful, but something in the foreground is disturbing.

Accepted Answer

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

Question 14

Identify the quantity and quality of the following statement. ($\exists$x)(Sx • ~Px)

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 15

Identify the quantity and quality of the following statement form. There is an S that is a P.

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 16

Symbolize the following statement. Some rules of logic are hard to remember.

Accepted Answer

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

Question 17

Pa is called a(n) _____ sentence and the constant "a" 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 18

In the following proof, which justification is correct for line 5? $\begin{array}{llcc}
  \text { (1) $ (x)[\operatorname{Ix}\supset(\mathrm{T} x x \supset H x)] $ } & & \text { Premise }  \ 
 \text {(2) $ (x)(\mathrm{H} x \supset \mathrm{D} x) \cdot(y) \sim \mathrm{D} y $  } && \text { Premise/Conclusion } \
& \text { $/(x)(\exists y) \sim(\mathrm{I} y \cdot \mathrm{Tyx})$ } &\
 \text { (3) $ (x)(\mathrm{H} x \supset \mathrm{D} x) $ } && \text { $ 2 \operatorname{Simp} $ } \
 \text { (4) $ (y) \sim D y $ } && \text {  $ 2 \operatorname{Simp} $} \
 \text { (5) $ \mathrm{Ia} \supset(\mathrm{Taa} \supset \mathrm{Ha}) $ } &\
\end{array}$

Accepted Answer

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

Question 19

Which of the following is the universal 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 20

Symbolize the following statement. No triangles have four angles.

Accepted Answer

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

Symbolize the following statement. At least one U.S.president was a Quaker.

The following inference is an application of which rule? (y)Gy.Therefore, Gb.

The following inference is an application of which rule? ~( $\exists$ y)~(My • Na).Therefore, (y)(My • Na).

The following inference is an application of which rule? (z)(Az $\supset$ Bd).Therefore, Ad $\supset$ Bd.

Symbolize the following statement. Only skydivers with much experience perform in thrill shows.

Identify the quantity and quality of the following statement form. Everyone likes to discuss the weather.

Which of the following is the existential instantiation rule?

Symbolize the following statement. All green or yellow vegetables are nutritious.

Symbolize the following statement. The painting is beautiful, but something in the foreground is disturbing.

Identify the quantity and quality of the following statement. ( $\exists$ x)(Sx • ~Px)

Identify the quantity and quality of the following statement form. There is an S that is a P.

Symbolize the following statement. Some rules of logic are hard to remember.

Pa is called a(n) _ sentence and the constant "a" is said to be _.

Which of the following is the universal generalization rule?

Symbolize the following statement. No triangles have four angles.

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

Symbolize the following statement. At least one U.S.president was a Quaker.

The following inference is an application of which rule? (y)Gy.Therefore, Gb.

The following inference is an application of which rule? ~( ∃\exists∃ y)~(My • Na).Therefore, (y)(My • Na).

The following inference is an application of which rule? (z)(Az ⊃\supset⊃ Bd).Therefore, Ad ⊃\supset⊃ Bd.

Symbolize the following statement. Only skydivers with much experience perform in thrill shows.

Identify the quantity and quality of the following statement form. Everyone likes to discuss the weather.

Which of the following is the existential instantiation rule?

Symbolize the following statement. All green or yellow vegetables are nutritious.

Symbolize the following statement. The painting is beautiful, but something in the foreground is disturbing.

Identify the quantity and quality of the following statement. ( ∃\exists∃ x)(Sx • ~Px)

Identify the quantity and quality of the following statement form. There is an S that is a P.

Symbolize the following statement. Some rules of logic are hard to remember.

Pa is called a(n) _____ sentence and the constant "a" is said to be _____.

Which of the following is the universal generalization rule?

Symbolize the following statement. No triangles have four angles.

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

The following inference is an application of which rule? ~( $\exists$ y)~(My • Na).Therefore, (y)(My • Na).

The following inference is an application of which rule? (z)(Az $\supset$ Bd).Therefore, Ad $\supset$ Bd.

Identify the quantity and quality of the following statement. ( $\exists$ x)(Sx • ~Px)

Pa is called a(n) _ sentence and the constant "a" is said to be _.