Question 1

Quantifier negation is an equivalence rule.

Accepted Answer

A) True 
 B)False

Question 2

Every invalid argument in predicate logic can be shown to be invalid by using the finite universe method.

Accepted Answer

A) True 
 B)False

Question 3

In ($x)Fx • Gx the variable in Gx falls within the scope of the existential quantifier.

Accepted Answer

A) True 
 B)False

Question 4

Symbols list
You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$
Symbolize this statement using the scheme of abbreviation provided: If anyone is good at baseball, Babe
Ruth is. (Px: x is a person; Gx: x is good at baseball; b: Babe Ruth)

Accepted Answer

($x)(Px • Gx) → Gb
A

Question 5

One can correctly move from Fbx to ($x)Fxx by EG.

Accepted Answer

A) True 
 B)False

Question 6

Symbols list
You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$
Symbolize this statement using the scheme of abbreviation provided: Cats are smarter than dogs. (Cx: x is
a cat; Dx: x is a dog; Sxy: x is smarter than y)

Accepted Answer

(x)[Cx → (y)(Dy → Sx

Question 7

"Being the sibling of" is an irreflexive relation.

Accepted Answer

A) True 
 B)False

Question 8

When using the finite universe method for a two-object universe (containing a and b), the statement (x)Fx would be translated as

Accepted Answer

A)  Fa ⋁ Fb. B. Fa • Fb. 
C)  Fa. 
D)  Fb. 
A)  Fa ⋁ Fb. B. Fa • Fb. 
C)  Fa. 
D)  Fb.

Question 9

Symbols list
You may use the list below to copy-and-paste symbols into your answer as needed.
→;↔;•;~;⋁;\;≠;$
Symbolize the following, using the scheme of abbreviation provided: The United States is the only
industrialized country that uses the death penalty. (Ix: x is an industrialized country; Dx: x uses the death
penalty; s: The United States)

Accepted Answer

(Is • Ds)

Question 10

Which of the following can be validly inferred from Bb • ~Ba by Existential Generalization?

Accepted Answer

A)  ($y)By • ~Ba 
B)  ($x)Bb • ~Bx 
C)  ($x)(Bb • ~Bx) 
D)  ($x)~Bx 
A)  ($y)By • ~Ba 
B)  ($x)Bb • ~Bx 
C)  ($x)(Bb • ~Bx) 
D)  ($x)~Bx

Question 11

We can validly infer (x)Ax → Ba from (x)Ax → Bb and a = b.

Accepted Answer

A) True 
 B)False

Question 12

Symbols list
You may use the list below to copy-and-paste symbols into your answer as needed.
→;↔;•;~;⋁;\;≠;$
Symbolize this statement using the scheme of abbreviation provided: Mark Twain wrote Huckleberry
Finn. (Wxy: x wrote y; t: Mark Twain; h: Huckleberry Finn)

Accepted Answer

The answer of Symbols list
You may use the list below...

Question 13

"Everyone has a mother" can be symbolized as (x)(Px → (y)(Py • Myx)), where Px: x is a person, and
Mxy: x is the mother of y.

Accepted Answer

A) True 
 B)False

Question 14

All of the following are well-formed formulas of predicate logic except

Accepted Answer

A)  (y)(Ay ⋁ ($y)By) 
B)  ((y)Ay ⋁ ($y)By) 
C)  (y)(x)(Ay ⋁ Bx) 
D)  Ay ⋁ Bx 
A)  (y)(Ay ⋁ ($y)By) 
B)  ((y)Ay ⋁ ($y)By) 
C)  (y)(x)(Ay ⋁ Bx) 
D)  Ay ⋁ Bx

Question 15

Where Sxy: x is shorter than y, ($x)(y)Sxy says

Accepted Answer

A)  everyone is shorter than someone. 
B)  someone is shorter than everyone. 
C)  everyone is such that someone is shorter. 
D)  someone is such that everyone is shorter. 
A)  everyone is shorter than someone. 
B)  someone is shorter than everyone. 
C)  everyone is such that someone is shorter. 
D)  someone is such that everyone is shorter.

Question 16

"Something creates everything except itself" can best be symbolized (Cxy: x creates y) as

Accepted Answer

A)  ($x)(y)Cxy. 
B)  ($x)[(y)Cxy • ~Cxx]. 
C)  ($x)[~Cxx • (y)(~y = x → Cxy)]. 
D)  ($x)(y)Cxy • ($x)~Cxx. 
A)  ($x)(y)Cxy. 
B)  ($x)[(y)Cxy • ~Cxx]. 
C)  ($x)[~Cxx • (y)(~y = x → Cxy)]. 
D)  ($x)(y)Cxy • ($x)~Cxx.

Question 17

"Only Oswald assassinated Kennedy" can best be symbolized (o: Oswald; k: Kennedy; Axy: x assassinated y) as

Accepted Answer

A)  Aok • (x)(Axk → x = o). 
B)  (x)(Axk → x = o). 
C)  ($x)Axk • (x)(Axk → x = k). 
D)  Aok. 
A)  Aok • (x)(Axk → x = o). 
B)  (x)(Axk → x = o). 
C)  ($x)Axk • (x)(Axk → x = k). 
D)  Aok.

Question 18

Symbols list
You may use the list below to copy-and-paste symbols into your answer as needed.
→;↔;•;~;⋁;\;≠;$
Symbolize the following, using the scheme of abbreviation provided: There are at least two candidates for
president. (Px: x is a candidate for president)

Accepted Answer

($x)($y)((

Question 19

For Existential Instantiation, the constant we instantiate to may not occur earlier in our proof.

Accepted Answer

A) True 
 B)False

Question 20

Which of the following may be validly inferred from ~($x)Fx?

Accepted Answer

A)  (x)~Fx 
B)  ($x)~Fx 
C)  ($x)Fx 
D)  ~(x)~Fx 
A)  (x)~Fx 
B)  ($x)~Fx 
C)  ($x)Fx 
D)  ~(x)~Fx

Quantifier negation is an equivalence rule.

Every invalid argument in predicate logic can be shown to be invalid by using the finite universe method.

In ($x)Fx • Gx the variable in Gx falls within the scope of the existential quantifier.

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize this statement using the scheme of abbreviation provided: If anyone is good at baseball, Babe Ruth is. (Px: x is a person; Gx: x is good at baseball; b: Babe Ruth)

One can correctly move from Fbx to ($x)Fxx by EG.

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize this statement using the scheme of abbreviation provided: Cats are smarter than dogs. (Cx: x is a cat; Dx: x is a dog; Sxy: x is smarter than y)

"Being the sibling of" is an irreflexive relation.

When using the finite universe method for a two-object universe (containing a and b), the statement (x)Fx would be translated as

Which of the following can be validly inferred from Bb • ~Ba by Existential Generalization?

We can validly infer (x)Ax → Ba from (x)Ax → Bb and a = b.

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize this statement using the scheme of abbreviation provided: Mark Twain wrote Huckleberry Finn. (Wxy: x wrote y; t: Mark Twain; h: Huckleberry Finn)

"Everyone has a mother" can be symbolized as (x)(Px → (y)(Py • Myx)), where Px: x is a person, and Mxy: x is the mother of y.

All of the following are well-formed formulas of predicate logic except

Where Sxy: x is shorter than y, ($x)(y)Sxy says

"Something creates everything except itself" can best be symbolized (Cxy: x creates y) as

"Only Oswald assassinated Kennedy" can best be symbolized (o: Oswald; k: Kennedy; Axy: x assassinated y) as

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize the following, using the scheme of abbreviation provided: There are at least two candidates for president. (Px: x is a candidate for president)

For Existential Instantiation, the constant we instantiate to may not occur earlier in our proof.

Which of the following may be validly inferred from ~($x)Fx?

Basic Concepts

Identifying Arguments

Logic and Language

Informal Fallacies

Categorical Logic: Statements

Categorical Logic: Syllogisms

Statement Logic: Truth Tables

Statement Logic: Proofs

Inductive Logic

Filters

Exam 9: Predicate Logic

Quantifier negation is an equivalence rule.

Every invalid argument in predicate logic can be shown to be invalid by using the finite universe method.

In ($x)Fx • Gx the variable in Gx falls within the scope of the existential quantifier.

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize this statement using the scheme of abbreviation provided: If anyone is good at baseball, Babe Ruth is. (Px: x is a person; Gx: x is good at baseball; b: Babe Ruth)

One can correctly move from Fbx to ($x)Fxx by EG.

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize this statement using the scheme of abbreviation provided: Cats are smarter than dogs. (Cx: x is a cat; Dx: x is a dog; Sxy: x is smarter than y)

"Being the sibling of" is an irreflexive relation.

When using the finite universe method for a two-object universe (containing a and b), the statement (x)Fx would be translated as

Which of the following can be validly inferred from Bb • ~Ba by Existential Generalization?

We can validly infer (x)Ax → Ba from (x)Ax → Bb and a = b.

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize this statement using the scheme of abbreviation provided: Mark Twain wrote Huckleberry Finn. (Wxy: x wrote y; t: Mark Twain; h: Huckleberry Finn)

"Everyone has a mother" can be symbolized as (x)(Px → (y)(Py • Myx)), where Px: x is a person, and Mxy: x is the mother of y.

All of the following are well-formed formulas of predicate logic except

Where Sxy: x is shorter than y, ($x)(y)Sxy says

"Something creates everything except itself" can best be symbolized (Cxy: x creates y) as

"Only Oswald assassinated Kennedy" can best be symbolized (o: Oswald; k: Kennedy; Axy: x assassinated y) as

Symbols list You may use the list below to copy-and-paste symbols into your answer as needed. →;↔;•;~;⋁;\;≠;$ Symbolize the following, using the scheme of abbreviation provided: There are at least two candidates for president. (Px: x is a candidate for president)

For Existential Instantiation, the constant we instantiate to may not occur earlier in our proof.

Which of the following may be validly inferred from ~($x)Fx?

Basic Concepts

Identifying Arguments

Logic and Language

Informal Fallacies

Categorical Logic: Statements

Categorical Logic: Syllogisms

Statement Logic: Truth Tables

Statement Logic: Proofs

Inductive Logic

Filters