Question 1

The statement Fa 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 2

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

Accepted Answer

A) 1 Taut 
B) 2 CP 
C) 2 Simp 
D) 2 RA 
E) None of these answers are correct. 
A) 1 Taut 
B) 2 CP 
C) 2 Simp 
D) 2 RA 
E) None of these answers are correct.

Question 3

($\exists$x)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 4

The statement Fa $\supset$Ga 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

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { P } x = x$ is a piece of paper$\quad $$\quad $$\quad $$W x = x$ is colored white
$( \exists x ) ( \mathrm { Px } \cdot \mathrm { W } x )$

Accepted Answer

A) All pieces of paper are colored white. 
B) No pieces of paper are colored white. 
C) Some pieces of paper are colored white. 
D) Some pieces of paper are not colored white. 
E) None of these answers are correct. 
A) All pieces of paper are colored white. 
B) No pieces of paper are colored white. 
C) Some pieces of paper are colored white. 
D) Some pieces of paper are not colored white. 
E) None of these answers are correct.

Question 6

The statement [(Da • Ra) • (Nb $\bigvee$ La)] $\supset$ (Ra • Sa) 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 7

Symbolize the following statement. Some Egyptians are members of the Muslim Brotherhood.

Accepted Answer

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

Question 8

Symbolize the following statement. Most insects hatch from eggs.

Accepted Answer

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

Question 9

Identify the type of statement represented by the following. Pa

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 10

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

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 11

Symbolize the following statement. Someone will win if and only if a winning ticket was played.

Accepted Answer

A) (x)(Px $\supset$ Wx) $\equiv$ (y)(Wy $\supset$ Py) 
B) ($\exists$x)(Px $\supset$ Wx) $\equiv$ ($\exists$y)(Wy $\supset$ Py) 
C) ($\exists$x)(Px • Wx) $\supset$$\exists$y)(Wy • Py) 
D) ($\exists$x)(Px • Wx) • ($\exists$y)(Wy • Py) 
E) None of these answers are correct. 
A) (x)(Px $\supset$ Wx) $\equiv$ (y)(Wy $\supset$ Py) 
B) ($\exists$x)(Px $\supset$ Wx) $\equiv$ ($\exists$y)(Wy $\supset$ Py) 
C) ($\exists$x)(Px • Wx) $\supset$$\exists$y)(Wy • Py) 
D) ($\exists$x)(Px • Wx) • ($\exists$y)(Wy • Py) 
E) None of these answers are correct.

Question 12

(y)By is called a(n) _____ sentence and the variable y 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

The statement Mc 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 14

Identify the quantity and quality of the following statement form. There is an S that is not 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 15

In the following proof, which justification is correct for line 3? $\begin{array}{llcc}
  \text { (1) \( (z)(\mathrm{I} z \supset \mathrm{K} z) $ } && \text {  Premise}  \
 \text {$\text { (2) (?y) } I y$  } & \text {$/(\exists x) \mathrm{K} x$ }& \text {Premise/Conclusion  }\
 \text {  (3) Ic} &\

\end{array}\)

Accepted Answer

A) 1, 2 MT 
B) 2 EI 
C) 2 Bicon 
D) 1 Contra 
E) None of these answers are correct. 
A) 1, 2 MT 
B) 2 EI 
C) 2 Bicon 
D) 1 Contra 
E) None of these answers are correct.

Question 16

The statement Aa 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

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

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 18

The statement Mb 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 19

Symbolize the following statement. Some courses are neither difficult nor boring.

Accepted Answer

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

Question 20

Symbolize the following statement. No car is both powerful and fuel efficient.

Accepted Answer

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

The statement Fa is which kind of statement?

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

The statement Fa $\supset$ Ga is which kind of statement?

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { P } x = x$ is a piece of paper $\quad$ $\quad$ $\quad$ $W x = x$ is colored white $( \exists x ) ( \mathrm { Px } \cdot \mathrm { W } x )$

The statement [(Da • Ra) • (Nb $\bigvee$ La)] $\supset$ (Ra • Sa) is which kind of statement?

Symbolize the following statement. Some Egyptians are members of the Muslim Brotherhood.

Symbolize the following statement. Most insects hatch from eggs.

Identify the type of statement represented by the following. Pa

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

Symbolize the following statement. Someone will win if and only if a winning ticket was played.

(y)By is called a(n) _ sentence and the variable y is said to be _.

The statement Mc is which kind of statement?

Identify the quantity and quality of the following statement form. There is an S that is not P.

The statement Aa is which kind of statement?

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

The statement Mb is which kind of statement?

Symbolize the following statement. Some courses are neither difficult nor boring.

Symbolize the following statement. No car is both powerful and fuel efficient.

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

The statement Fa is which kind of statement?

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

The statement Fa ⊃\supset⊃ Ga is which kind of statement?

Translate the following symbolized categorical statement into English using the provided key. Px=x\mathrm { P } x = xPx=x is a piece of paper \quad \quad \quad Wx=xW x = xWx=x is colored white (∃x)(Px⋅Wx)( \exists x ) ( \mathrm { Px } \cdot \mathrm { W } x )(∃x)(Px⋅Wx)

The statement [(Da • Ra) • (Nb ⋁\bigvee⋁ La)] ⊃\supset⊃ (Ra • Sa) is which kind of statement?

Symbolize the following statement. Some Egyptians are members of the Muslim Brotherhood.

Symbolize the following statement. Most insects hatch from eggs.

Identify the type of statement represented by the following. Pa

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

Symbolize the following statement. Someone will win if and only if a winning ticket was played.

(y)By is called a(n) _____ sentence and the variable y is said to be _____.

The statement Mc is which kind of statement?

Identify the quantity and quality of the following statement form. There is an S that is not P.

The statement Aa is which kind of statement?

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

The statement Mb is which kind of statement?

Symbolize the following statement. Some courses are neither difficult nor boring.

Symbolize the following statement. No car is both powerful and fuel efficient.

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

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

The statement Fa $\supset$ Ga is which kind of statement?

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { P } x = x$ is a piece of paper $\quad$ $\quad$ $\quad$ $W x = x$ is colored white $( \exists x ) ( \mathrm { Px } \cdot \mathrm { W } x )$

The statement [(Da • Ra) • (Nb $\bigvee$ La)] $\supset$ (Ra • Sa) is which kind of statement?

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

(y)By is called a(n) _ sentence and the variable y is said to be _.

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