Question 1

Symbolize the following statement form. Many 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 2

In the following proof, which justification is correct for line 3? $\begin{array}{llcc}
  \text { (1) $ (x)(\mathrm{U} x \supset \mathrm{T} x) $ } & \text { $/(\exists x)(U x \supset T x)$ }& \text {Premise/Conclusion  }  \
 \text {(2) $ \mathrm{Ua} \supset \mathrm{Ta} $  } && \text {  $1 \mathrm{UI}$}\
 \text {(3) $ (\exists x)(\mathrm{U} x \supset \mathrm{T} x) $  } &\
\end{array}$

Accepted Answer

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

Question 3

Symbolize the following statement. Many types of cactus plants have lost true leaves.

Accepted Answer

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

Question 4

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 5

Symbolize the following statement. All pentagons have five sides.

Accepted Answer

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

Question 6

Identify the quantity and quality of the following statement form. Every S is 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 7

The statement (x)Fx $\supset$ (x)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 8

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 9

(x)Nz $\supset$ Pa 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 10

Symbolize the following statement. Some politicians are corrupt.

Accepted Answer

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

Question 11

Symbolize the following statement. Tom bought a car and it's a lemon.

Accepted Answer

A) (x)[(Cx • Btx) • Lx] 
B) ($\exists$x)[(Cx • Bxt) • Lx] 
C) ($\exists$x)[(Cx • Btx) • Lx] 
D) (Cx • Btx) • Lx 
E) None of these answers are correct. 
A) (x)[(Cx • Btx) • Lx] 
B) ($\exists$x)[(Cx • Bxt) • Lx] 
C) ($\exists$x)[(Cx • Btx) • Lx] 
D) (Cx • Btx) • Lx 
E) None of these answers are correct.

Question 12

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { C } x = x$ is a comet$\quad $$\quad $$\quad $$\quad $$\mathrm { E } x = x$ travels in an elliptical orbit
$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$( x ) ( \mathrm { C } x \supset \mathrm { E } x )$

Accepted Answer

A) All comets travel in elliptical orbits. 
B) No comets travel in elliptical orbits. 
C) Some comets travel in elliptical orbits. 
D) Some comets do not travel in elliptical orbits. 
E) None of these answers are correct. 
A) All comets travel in elliptical orbits. 
B) No comets travel in elliptical orbits. 
C) Some comets travel in elliptical orbits. 
D) Some comets do not travel in elliptical orbits. 
E) None of these answers are correct.

Question 13

Symbolize the following statement. Some black cats are good luck.

Accepted Answer

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

Question 14

The statement (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

Question 15

In the following proof, which justification is correct for line 4? $\begin{array}{llcc}
  \text {(1) $ (x)[(\mathrm{C} x \supset \mathrm{D} x) \supset \sim \mathrm{E} x] $  } && \text { Premise }  \
 \text { (2) $ \mathrm{Ea} $ } & \text {$/ \sim(\mathrm{Ca} \cdot \mathrm{Da})$  }& \text {  Premise/Conclusion}\
 \text { (3) $ \mathrm{Ca} \cdot \mathrm{Da} $ } && \text { Assumption }\
 \text { (4) $ (\mathrm{Ca} \supset \mathrm{Da}) \supset \sim \mathrm{Ea} $ } &\
\end{array}$

Accepted Answer

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

Question 16

Symbolize the following statement. Some mathematicians are good teachers.

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 17

Symbolize the following statement. All quadratic functions have parabolic graphs.

Accepted Answer

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

Question 18

In the following proof, which justification is correct for line 4? $\begin{array}{llcc}
  \text {(1) $ (y)(\mathrm{S} y \supset \mathrm{G} y) $} && \text {Premise  }   \
 \text { (2) $ \mathrm{Sb} $ } & \text {$/(\exists x) \mathrm{G} x$ } & \text { Premise/Conclusion } \
 \text { (3) $ \mathrm{Sb} \Rightarrow \mathrm{Gb} $} && \text {$1 \mathrm{UI}$  } \
 \text { (4) $ \mathrm{Gb} $ } &\
\end{array}$

Accepted Answer

A) 2 QN 
B) 2 Simp 
C) 2, 3 MP 
D) Assumption 
E) None of these answers are correct. 
A) 2 QN 
B) 2 Simp 
C) 2, 3 MP 
D) Assumption 
E) None of these answers are correct.

Question 19

`Which of the following is the quantifier-negation rule?

Accepted Answer

A)  $ (x)(\ldots x \ldots) $. Therefore, $ (\ldots $ a ... $ ) $ 
B)  $ \sim(x)(\ldots x \ldots) $. Therefore, $ (\exists x) \sim(\ldots x \ldots) $ 
C)  $ (\ldots $ a .... $ ) $. Therefore, $ (\exists x)(\ldots x \ldots) $ 
D)  $ (\exists x)(\ldots x \ldots) $ Therefore, $ (\ldots \mathrm{a} \ldots) $ 
E)  $ (\ldots $ a ... ) Therefore, $ (x)(\ldots x \ldots) $ 
A)  $ (x)(\ldots x \ldots) $. Therefore, $ (\ldots $ a ... $ ) $ 
B)  $ \sim(x)(\ldots x \ldots) $. Therefore, $ (\exists x) \sim(\ldots x \ldots) $ 
C)  $ (\ldots $ a .... $ ) $. Therefore, $ (\exists x)(\ldots x \ldots) $ 
D)  $ (\exists x)(\ldots x \ldots) $ Therefore, $ (\ldots \mathrm{a} \ldots) $ 
E)  $ (\ldots $ a ... ) Therefore, $ (x)(\ldots x \ldots) $

Question 20

The following inference is an application of which rule? ($\exists$x)Mx.Therefore, Ma.

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

Symbolize the following statement form. Many A are B.

Symbolize the following statement. Many types of cactus plants have lost true leaves.

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

Symbolize the following statement. All pentagons have five sides.

Identify the quantity and quality of the following statement form. Every S is P.

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

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

(x)Nz $\supset$ Pa is called a(n) _ sentence and the variable z is said to be _.

Symbolize the following statement. Some politicians are corrupt.

Symbolize the following statement. Tom bought a car and it's a lemon.

Symbolize the following statement. Some black cats are good luck.

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

Symbolize the following statement. Some mathematicians are good teachers.

Symbolize the following statement. All quadratic functions have parabolic graphs.

`Which of the following is the quantifier-negation rule?

The following inference is an application of which rule? ( $\exists$ x)Mx.Therefore, Ma.

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 form. Many A are B.

Symbolize the following statement. Many types of cactus plants have lost true leaves.

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

Symbolize the following statement. All pentagons have five sides.

Identify the quantity and quality of the following statement form. Every S is P.

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

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

(x)Nz ⊃\supset⊃ Pa is called a(n) _____ sentence and the variable z is said to be _____.

Symbolize the following statement. Some politicians are corrupt.

Symbolize the following statement. Tom bought a car and it's a lemon.

Symbolize the following statement. Some black cats are good luck.

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

Symbolize the following statement. Some mathematicians are good teachers.

Symbolize the following statement. All quadratic functions have parabolic graphs.

`Which of the following is the quantifier-negation rule?

The following inference is an application of which rule? ( ∃\exists∃ x)Mx.Therefore, Ma.

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

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

(x)Nz $\supset$ Pa is called a(n) _ sentence and the variable z is said to be _.

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

The following inference is an application of which rule? ( $\exists$ x)Mx.Therefore, Ma.