Question 1

A relation R is symmetrical just in case if a bears R to b then b bears R to a.

Accepted Answer

A) True 
 B)False

Question 2

Which of the following is the best symbolization of "Every number is either odd or even"? (Nx: x is a number; Ox: x is odd; Ex: x is even.)

Accepted Answer

A)  (x)(Nx → (Ox • Ex)) B. (x)(Nx ⋁ (Ox • Ex)) 
C)  (x)(Nx → (Ox ⋁Ex)) 
D)  (x)(Nx • (Ox ⋁ Ex)) 
A)  (x)(Nx → (Ox • Ex)) B. (x)(Nx ⋁ (Ox • Ex)) 
C)  (x)(Nx → (Ox ⋁Ex)) 
D)  (x)(Nx • (Ox ⋁ Ex))

Question 3

Correctly using Universal Generalization on Bc → Ba yields (x)Bx → Ba.

Accepted Answer

A) True 
 B)False

Question 4

From ($x)(y)Fxy we can validly infer (y)Fay, assuming that "a" is not found earlier in the proof.

Accepted Answer

A) True 
 B)False

Question 5

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 Edison isn't an inventor, then no
one is an inventor. (e: Edison; Ix: x is an inventor; Px: x is a person)

Accepted Answer

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

Question 6

~Ab is a well-formed formula.

Accepted Answer

A) True 
 B)False

Question 7

Given that a = b, which of the following is an incorrect application of Leibniz's law?

Accepted Answer

A)  inferring Ca • Da from Cb • Da 
B)  inferring Ab → Db from Aa → Da 
C)  inferring (w)Bww from (w)Bwa 
D)  inferring Lca → Lac from Lcb → Lbc 
A)  inferring Ca • Da from Cb • Da 
B)  inferring Ab → Db from Aa → Da 
C)  inferring (w)Bww from (w)Bwa 
D)  inferring Lca → Lac from Lcb → Lbc

Question 8

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: Every athlete wants to win an
Olympic medal. (Ax: x is an athlete; Wxy: x wants to win y; Ox: x is an Olympic medal)

Accepted Answer

(x)[Ax → (

Question 9

Which of the following is a correct use of UI?

Accepted Answer

A)  inferring (x)Fax from (y)(x)Fxy B. inferring ($y)Fay from ($y)(x)Fxy 
C)  inferring ($x)(Fx → Fxa) from ($x)(Fx → (y)Fxy) 
D)  inferring (y)(Fy → Ga) from (x)(y)(Fy → Gx) 
A)  inferring (x)Fax from (y)(x)Fxy B. inferring ($y)Fay from ($y)(x)Fxy 
C)  inferring ($x)(Fx → Fxa) from ($x)(Fx → (y)Fxy) 
D)  inferring (y)(Fy → Ga) from (x)(y)(Fy → Gx)

Question 10

In (y)s = y • Ly, the scope of the quantifier is s = y.

Accepted Answer

A) True 
 B)False

Question 11

In which of the following is the variable "x" free?

Accepted Answer

A)  ($x)Fx • Gy 
B)  ($x)(y)(Gy → Fx) 
C)  (x)((Fx • Gx) → Hx) 
D)  Fx • (x)(Gx → Hx) 
A)  ($x)Fx • Gy 
B)  ($x)(y)(Gy → Fx) 
C)  (x)((Fx • Gx) → Hx) 
D)  Fx • (x)(Gx → Hx)

Question 12

A relation R is transitive when things bear R to themselves.

Accepted Answer

A) True 
 B)False

Question 13

According to Leibniz's law, if x = y then y = x.

Accepted Answer

A) True 
 B)False

Question 14

(x)Fx is a universally quantified statement.

Accepted Answer

A) True 
 B)False

Question 15

In general, the inference from a universal statement to its corresponding particular is invalid when their subject terms denote an empty class.

Accepted Answer

A) True 
 B)False

Question 16

The finite universe method involves

Accepted Answer

A)  describing a possible situation where the premises of an argument are true and the conclusion of the argument is true. 
B)  describing a possible situation where the conclusion of the argument is true. 
C)  describing a possible situation where the premises are false. 
D)  describing a possible situation where the premises are true and the conclusion is false. 
A)  describing a possible situation where the premises of an argument are true and the conclusion of the argument is true. 
B)  describing a possible situation where the conclusion of the argument is true. 
C)  describing a possible situation where the premises are false. 
D)  describing a possible situation where the premises are true and the conclusion is false.

Question 17

(x)(Hx → ~Ix) is a universal negative statement.

Accepted Answer

A) True 
 B)False

Question 18

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: No vampire is more cunning than
Dracula. (Vx: x is a vampire; Cxy: x is more cunning than y; d: Dracula)

Accepted Answer

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

Question 19

Which of the following can be inferred from ~a = b by symmetry?

Accepted Answer

A)  ~b = a 
B)  a = ~b 
C)  b = ~a 
D)  ~b = ~a 
A)  ~b = a 
B)  a = ~b 
C)  b = ~a 
D)  ~b = ~a

Question 20

Which of the following is the best translation into symbols of the sentence "All fickle people are difficult to please"? (Fx: x is a fickle person, and Dx: x is a person difficult to please.)

Accepted Answer

A)  (x)(Fx • Dx) 
B)  (x)(Fx → Dx) 
C)  (x)Fx → Dx 
D)  (x)(Fx ↔ Dx) 
A)  (x)(Fx • Dx) 
B)  (x)(Fx → Dx) 
C)  (x)Fx → Dx 
D)  (x)(Fx ↔ Dx)

A relation R is symmetrical just in case if a bears R to b then b bears R to a.

Which of the following is the best symbolization of "Every number is either odd or even"? (Nx: x is a number; Ox: x is odd; Ex: x is even.)

Correctly using Universal Generalization on Bc → Ba yields (x)Bx → Ba.

From ($x)(y)Fxy we can validly infer (y)Fay, assuming that "a" is not found earlier in the proof.

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 Edison isn't an inventor, then no one is an inventor. (e: Edison; Ix: x is an inventor; Px: x is a person)

~Ab is a well-formed formula.

Given that a = b, which of the following is an incorrect application of Leibniz's law?

Which of the following is a correct use of UI?

In (y)s = y • Ly, the scope of the quantifier is s = y.

In which of the following is the variable "x" free?

A relation R is transitive when things bear R to themselves.

According to Leibniz's law, if x = y then y = x.

(x)Fx is a universally quantified statement.

In general, the inference from a universal statement to its corresponding particular is invalid when their subject terms denote an empty class.

The finite universe method involves

(x)(Hx → ~Ix) is a universal negative statement.

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: No vampire is more cunning than Dracula. (Vx: x is a vampire; Cxy: x is more cunning than y; d: Dracula)

Which of the following can be inferred from ~a = b by symmetry?

Which of the following is the best translation into symbols of the sentence "All fickle people are difficult to please"? (Fx: x is a fickle person, and Dx: x is a person difficult to please.)

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

A relation R is symmetrical just in case if a bears R to b then b bears R to a.

Which of the following is the best symbolization of "Every number is either odd or even"? (Nx: x is a number; Ox: x is odd; Ex: x is even.)

Correctly using Universal Generalization on Bc → Ba yields (x)Bx → Ba.

From ($x)(y)Fxy we can validly infer (y)Fay, assuming that "a" is not found earlier in the proof.

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 Edison isn't an inventor, then no one is an inventor. (e: Edison; Ix: x is an inventor; Px: x is a person)

~Ab is a well-formed formula.

Given that a = b, which of the following is an incorrect application of Leibniz's law?

Which of the following is a correct use of UI?

In (y)s = y • Ly, the scope of the quantifier is s = y.

In which of the following is the variable "x" free?

A relation R is transitive when things bear R to themselves.

According to Leibniz's law, if x = y then y = x.

(x)Fx is a universally quantified statement.

In general, the inference from a universal statement to its corresponding particular is invalid when their subject terms denote an empty class.

The finite universe method involves

(x)(Hx → ~Ix) is a universal negative statement.

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: No vampire is more cunning than Dracula. (Vx: x is a vampire; Cxy: x is more cunning than y; d: Dracula)

Which of the following can be inferred from ~a = b by symmetry?

Which of the following is the best translation into symbols of the sentence "All fickle people are difficult to please"? (Fx: x is a fickle person, and Dx: x is a person difficult to please.)

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