Question 1

Symbolize the following statement. Every teacher is a saint.

Accepted Answer

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

Question 2

In the following proof, which justification is correct for line 4? $\begin{array}{llcc}
  \text { (1) \( (x)[(T x \cup D x) \supset F x] $ } & \text {$I(x)(\mathrm{D} x \supset \mathrm{F} x)$  }& \text { Premise/Conclusion  }  \
 \text { (2) $ \mathrm{Da} $ } && \text {  Assumption}\
 \text {  (3) $ (\mathrm{Ta} \vee \mathrm{Da}) \supset \mathrm{Fa} $} && \text {  $ 1 \mathrm{UI} $ }\
 \text {(4) $ \mathrm{Ta} \cup \mathrm{Da} $  } &\

\end{array}\)

Accepted Answer

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

Question 3

The statement ~[($\exists$x)Fx • ~($\exists$x)Fx] 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 E

Question 4

Identify the quantity and quality of the following statement form. All babies cry.

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 5

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { B } x = x$ was an inductee into the Baseball Hall of Fame
$\quad $$\quad $$\quad $ $\mathrm { G } x = x$ was born in Georgia
$\quad $$\quad $$\quad $$\quad $$\quad $$( \exists x ) ( \mathrm { B } x \cdot \mathrm { G } x )$

Accepted Answer

A) All inductees into the Baseball Hall of Fame were born in Georgia. 
B) No inductees into the Baseball Hall of Fame were born in Georgia. 
C) Some inductees into the Baseball Hall of Fame were born in Georgia. 
D) Some inductees into the Baseball Hall of Fame were not born in Georgia. 
E) None of these answers are correct. 
A) All inductees into the Baseball Hall of Fame were born in Georgia. 
B) No inductees into the Baseball Hall of Fame were born in Georgia. 
C) Some inductees into the Baseball Hall of Fame were born in Georgia. 
D) Some inductees into the Baseball Hall of Fame were not born in Georgia. 
E) None of these answers are correct.

Question 6

Symbolize the following statement. Some baseball players do not take performance-enhancing drugs.

Accepted Answer

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

Question 7

Symbolize the following statement. Some people are lonely and sad.

Accepted Answer

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

Question 8

In the following proof, which justification is correct for line 6? $\begin{array}{llcc}
  \text { (1) $ (x)(U x \supset Y x) \cdot U a $ } & \text { $/(\exists x)(\mathrm{Y} x \cdot \mathrm{U} x)$ } & \text {Fremise/Conclusion  }   \
 \text {(2) $ (x)(\mathrm{U} x \supset \mathrm{Y}) $  } && 1 \operatorname{Simp}  \
 \text { (3) $ \mathrm{Ua} $ } &&1 \operatorname{Simp}  \
 \text { (4) $ \mathrm{Ua} D \mathrm{Ya} $ } &&2 \mathrm{UI} \
 \text { (5) $ \mathrm{Ya} $ } &&3,4 \mathrm{MP}\
 \text {  (6) $ \mathrm{Ya} \cdot \mathrm{Ua} $} &\
\end{array}$

Accepted Answer

A) 5 Taut 
B) 5 Simp 
C) 5 Add 
D) 3, 5 Conj 
E) None of these answers are correct. 
A) 5 Taut 
B) 5 Simp 
C) 5 Add 
D) 3, 5 Conj 
E) None of these answers are correct.

Question 9

Symbolize the following statement. Some of Kepler's conclusions were mistaken.

Accepted Answer

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

Question 10

Px is called a(n) _____ sentence and the variable x 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 11

The statement (x)~Fx 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 12

In the following proof, which justification is correct for line 4? $\begin{array}{llcc}
  \text {(1) }(\exists y)\mathrm{Myyy  } & \text {$/(\exists x)(\exists y)(\exists z) \mathrm{M} x y z$  } &\text { Fremise/Conclusion }\
 \text { (2) Maaa } &&1 \mathrm{EI}\ 
 \text { (3) ( } \exists z \text { )Maaz } &&2 \mathrm{EG}\
\text { (4) }(\exists y)(\exists z) \mathrm{Mayz} &\
\end{array}$

Accepted Answer

A) 2 EG 
B) 3 QN 
C) 3 EG 
D) 3 Add 
E) None of these answers are correct. 
A) 2 EG 
B) 3 QN 
C) 3 EG 
D) 3 Add 
E) None of these answers are correct.

Question 13

Symbolize the following statement. Some monks were geneticists.

Accepted Answer

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

Question 14

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { C } x = x$ is a chemical element $\quad $$\quad $$\quad $$\quad $$\quad $$\mathrm { M } x = x$ is a metal
$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$( \exists x ) ( \mathrm { C } x \cdot \mathrm { M } x )$

Accepted Answer

A) All chemical elements are metals. 
B) No chemical elements are metals. 
C) Some chemical elements are metals. 
D) Some chemical elements are not metals. 
E) None of these answers are correct. 
A) All chemical elements are metals. 
B) No chemical elements are metals. 
C) Some chemical elements are metals. 
D) Some chemical elements are not metals. 
E) None of these answers are correct.

Question 15

Symbolize the following statement. Many types of mushrooms are not poisonous to humans.

Accepted Answer

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

Question 16

The statement (x)(Fx $\supset$ Gx) 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 17

Symbolize the following statement. Construction crews are noisy.

Accepted Answer

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

Question 18

The following inference is an application of which rule? Na.Therefore, (x)Nx.

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 19

The statement ~Mc $\equiv$ Bm 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 20

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

Accepted Answer

A) 1 UG 
B) 1 Simp 
C) Assumption 
D) 3 Add 
E) None of these answers are correct. 
A) 1 UG 
B) 1 Simp 
C) Assumption 
D) 3 Add 
E) None of these answers are correct.

Symbolize the following statement. Every teacher is a saint.

In the following proof, which justification is correct for line 4? (1) (x)[(T x \cup D x) \supset F x] I(x)(x\supsetx) Premise/Conclusion (2) Assumption (3) (\vee)\supset 1 (4) \cup

The statement ~[( $\exists$ x)Fx • ~( $\exists$ x)Fx] is which kind of statement?

Identify the quantity and quality of the following statement form. All babies cry.

Symbolize the following statement. Some baseball players do not take performance-enhancing drugs.

Symbolize the following statement. Some people are lonely and sad.

In the following proof, which justification is correct for line 6? (1) (x)(U x \supset Y x) \cdot U a /(\existsx)(x\cdotx) Fremise/Conclusion (2) (x)(x\supset) 1 Simp (3) 1 Simp (4) D 2 (5) 3,4 (6) \cdot

Symbolize the following statement. Some of Kepler's conclusions were mistaken.

Px is called a(n) _ sentence and the variable x is said to be _.

The statement (x)~Fx is which kind of statement?

Symbolize the following statement. Some monks were geneticists.

Symbolize the following statement. Many types of mushrooms are not poisonous to humans.

The statement (x)(Fx $\supset$ Gx) is which kind of statement?

Symbolize the following statement. Construction crews are noisy.

The following inference is an application of which rule? Na.Therefore, (x)Nx.

The statement ~Mc $\equiv$ Bm is which kind of statement?

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. Every teacher is a saint.

In the following proof, which justification is correct for line 4? (1) (x)[(T x \cup D x) \supset F x] I(x)(x\supsetx) Premise/Conclusion (2) Assumption (3) (\vee)\supset 1 (4) \cup

The statement ~[( ∃\exists∃ x)Fx • ~( ∃\exists∃ x)Fx] is which kind of statement?

Identify the quantity and quality of the following statement form. All babies cry.

Symbolize the following statement. Some baseball players do not take performance-enhancing drugs.

Symbolize the following statement. Some people are lonely and sad.

In the following proof, which justification is correct for line 6? (1) (x)(U x \supset Y x) \cdot U a /(\existsx)(x\cdotx) Fremise/Conclusion (2) (x)(x\supset) 1 Simp (3) 1 Simp (4) D 2 (5) 3,4 (6) \cdot

Symbolize the following statement. Some of Kepler's conclusions were mistaken.

Px is called a(n) _____ sentence and the variable x is said to be _____.

The statement (x)~Fx is which kind of statement?

Symbolize the following statement. Some monks were geneticists.

Symbolize the following statement. Many types of mushrooms are not poisonous to humans.

The statement (x)(Fx ⊃\supset⊃ Gx) is which kind of statement?

Symbolize the following statement. Construction crews are noisy.

The following inference is an application of which rule? Na.Therefore, (x)Nx.

The statement ~Mc ≡\equiv≡ Bm is which kind of statement?

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 statement ~[( $\exists$ x)Fx • ~( $\exists$ x)Fx] is which kind of statement?

Px is called a(n) _ sentence and the variable x is said to be _.

The statement (x)(Fx $\supset$ Gx) is which kind of statement?

The statement ~Mc $\equiv$ Bm is which kind of statement?