Question 1

Some poets are sensitive souls. Therefore, some poets are not insensitive souls.

Accepted Answer

A)  Invalid, illicit contraposition. 
B)  Invalid, illicit subcontrary. 
C)  Invalid, illicit subalternation. 
D)  Valid, no fallacy. 
E)  Invalid, illicit conversion. 
A)  Invalid, illicit contraposition. 
B)  Invalid, illicit subcontrary. 
C)  Invalid, illicit subalternation. 
D)  Valid, no fallacy. 
E)  Invalid, illicit conversion.

Question 2

It is false that all cowboys are romantic icons. Therefore, no cowboys are romantic icons.

Accepted Answer

A)  Valid, no fallacy. 
B)  Invalid, illicit subalternation. 
C)  Invalid, illicit contrary. 
D)  Invalid, illicit conversion. 
E)  Invalid, existential fallacy. 
A)  Valid, no fallacy. 
B)  Invalid, illicit subalternation. 
C)  Invalid, illicit contrary. 
D)  Invalid, illicit conversion. 
E)  Invalid, existential fallacy.

Question 3

All proponents of globalization are individuals unconcerned with world poverty. Therefore, all individuals concerned with world poverty are opponents of globalization.

Accepted Answer

A)  Valid. 
B)  Invalid, illicit conversion. 
C)  Invalid, illicit contrary. 
D)  Invalid, illicit obversion. 
E)  Invalid, illicit contraposition. 
A)  Valid. 
B)  Invalid, illicit conversion. 
C)  Invalid, illicit contrary. 
D)  Invalid, illicit obversion. 
E)  Invalid, illicit contraposition.

Question 4

It is false that some rare coins are worthless collectibles. Therefore, it is false that all rare coins are worthless collectibles.

Accepted Answer

A)  Invalid, illicit conversion. 
B)  Invalid, illicit subcontrary. 
C)  Invalid, illicit contrary. 
D)  Invalid, illicit subalternation. 
E)  Valid. 
A)  Invalid, illicit conversion. 
B)  Invalid, illicit subcontrary. 
C)  Invalid, illicit contrary. 
D)  Invalid, illicit subalternation. 
E)  Valid.

Question 5

No mint juleps are sour concoctions. Therefore, no sour concoctions are mint juleps.

Accepted Answer

A)  Invalid, illicit subalternation. 
B)  Invalid, illicit conversion. 
C)  Invalid, illicit contrary. 
D)  Invalid, illicit contraposition. 
E)  Valid, no fallacy. 
A)  Invalid, illicit subalternation. 
B)  Invalid, illicit conversion. 
C)  Invalid, illicit contrary. 
D)  Invalid, illicit contraposition. 
E)  Valid, no fallacy.

Question 6

Some crystal vases are not China teapots. Therefore, some China teapots are not crystal vases.

Accepted Answer

A)  Valid, no fallacy. 
B)  Invalid, illicit contrary. 
C)  Invalid, illicit contraposition. 
D)  Invalid, illicit conversion. 
E)  Invalid, illicit subalternation. 
A)  Valid, no fallacy. 
B)  Invalid, illicit contrary. 
C)  Invalid, illicit contraposition. 
D)  Invalid, illicit conversion. 
E)  Invalid, illicit subalternation.

Question 7

In each problem below you are given a statement, its truth value in parentheses, and an operation/relation to be performed on that statement.  You must identify the new statement and the truth value of the new statement. Take the Aristotelian standpoint and assume that ‘A’ and ‘B’ denote things that actually exist.
-No non-A are B. (T) Conversion

Accepted Answer

A)  No non-B are A. (Und.) 
B)  No A are non-B. (T) 
C)  No B are non-A. (T) 
D)  All non-A are non-B. (T) 
E)  All non-A are B. (F) 
A)  No non-B are A. (Und.) 
B)  No A are non-B. (T) 
C)  No B are non-A. (T) 
D)  All non-A are non-B. (T) 
E)  All non-A are B. (F)

Question 8

Given the categorical proposition "Some mathematicians are not topologists." If the quantity but not the quality is changed, the resulting proposition is:

Accepted Answer

A)  Some non-mathematicians are topologists. 
B)  Some mathematicians are topologists. 
C)  No mathematicians are topologists. 
D)  Some mathematicians are non-topologists. 
E)  All mathematicians are topologists. 
A)  Some non-mathematicians are topologists. 
B)  Some mathematicians are topologists. 
C)  No mathematicians are topologists. 
D)  Some mathematicians are non-topologists. 
E)  All mathematicians are topologists.

Question 9

It is false that all water sprites are charming nymphs. Therefore, some water sprites are not charming nymphs.

Accepted Answer

A)  Invalid, illicit subalternation. 
B)  Invalid, illicit subcontrary. 
C)  Invalid, existential fallacy. 
D)  Valid, no fallacy. 
E)  Invalid, illicit contrary. 
A)  Invalid, illicit subalternation. 
B)  Invalid, illicit subcontrary. 
C)  Invalid, existential fallacy. 
D)  Valid, no fallacy. 
E)  Invalid, illicit contrary.

Question 10

Not all parrots are colorful.

Accepted Answer

A)  Some parrots are not colorful birds. 
B)  Some parrots are colorful birds and some parrots are not colorful birds. 
C)  Some parrots are not colorful. 
D)  Some colorful birds are not parrots. 
E)  All parrots are not colorful birds. 
A)  Some parrots are not colorful birds. 
B)  Some parrots are colorful birds and some parrots are not colorful birds. 
C)  Some parrots are not colorful. 
D)  Some colorful birds are not parrots. 
E)  All parrots are not colorful birds.

Question 11

It is false that no high schools are institutions plagued by drunkenness. Therefore, it is false that some high schools are not institutions plagued by drunkenness.

Accepted Answer

A)  Invalid, illicit subalternation. 
B)  Invalid, illicit subcontrary. 
C)  Invalid, illicit contrary. 
D)  Invalid, illicit conversion. 
E)  Valid. 
A)  Invalid, illicit subalternation. 
B)  Invalid, illicit subcontrary. 
C)  Invalid, illicit contrary. 
D)  Invalid, illicit conversion. 
E)  Valid.

Question 12

It is false that some gothic cathedrals are not rich legacies. Therefore, some gothic cathedrals are rich legacies.

Accepted Answer

A)  Invalid, illicit conversion. 
B)  Invalid, illicit subcontrary. 
C)  Valid, no fallacy. 
D)  Invalid, illicit subalternation. 
E)  Invalid, existential fallacy. 
A)  Invalid, illicit conversion. 
B)  Invalid, illicit subcontrary. 
C)  Valid, no fallacy. 
D)  Invalid, illicit subalternation. 
E)  Invalid, existential fallacy.

Question 13

She sings whenever she is happy.

Accepted Answer

A)  All times she sings are times she is happy. 
B)  Some times she is happy are times she sings. 
C)  All times she is happy are times she sings. 
D)  All times she is not happy are times she does not sing. 
E)  All times she is happy she sings. 
A)  All times she sings are times she is happy. 
B)  Some times she is happy are times she sings. 
C)  All times she is happy are times she sings. 
D)  All times she is not happy are times she does not sing. 
E)  All times she is happy she sings.

Question 14

In each problem below you are given a statement, its truth value in parentheses, and an operation/relation to be performed on that statement.  You must identify the new statement and the truth value of the new statement. Take the Aristotelian standpoint and assume that ‘A’ and ‘B’ denote things that actually exist.
-All A are B. (T) Contrary

Accepted Answer

A)  No A are non-B. (T) 
B)  All B are A. (Und.) 
C)  Some A are B. (T) 
D)  No A are B. (Und.) 
E)  No A are B. (F) 
A)  No A are non-B. (T) 
B)  All B are A. (Und.) 
C)  Some A are B. (T) 
D)  No A are B. (Und.) 
E)  No A are B. (F)

Question 15

In each problem below you are given a statement, its truth value in parentheses, and an operation/relation to be performed on that statement.  You must identify the new statement and the truth value of the new statement. Take the Aristotelian standpoint and assume that ‘A’ and ‘B’ denote things that actually exist.
-Some A are not non-B. (F) Contradiction

Accepted Answer

A)  All A are non-B. (T) 
B)  Some A are non-B. (T) 
C)  Some B are not non-A. (F) 
D)  Some A are non-B. (T). 
E)  Some A are B. (T) 
A)  All A are non-B. (T) 
B)  Some A are non-B. (T) 
C)  Some B are not non-A. (F) 
D)  Some A are non-B. (T). 
E)  Some A are B. (T)

Question 16

Some weekend getaways are not relaxing vacations. Therefore, some weekend getaways are relaxing vacations.

Accepted Answer

A)  Invalid, illicit subalternation. 
B)  Invalid, illicit subcontrary. 
C)  Invalid, illicit contrary. 
D)  Invalid, illicit contraposition. 
E)  Valid, no fallacy. 
A)  Invalid, illicit subalternation. 
B)  Invalid, illicit subcontrary. 
C)  Invalid, illicit contrary. 
D)  Invalid, illicit contraposition. 
E)  Valid, no fallacy.

Question 17

Some non-A are non-B. (F) Some B are A.

Accepted Answer

A)  Conversion. (F) 
B)  Contraposition. (F) 
C)  Conversion. (Und.) 
D)  Subcontrary. (T) 
E)  Contraposition. (Und.) 
A)  Conversion. (F) 
B)  Contraposition. (F) 
C)  Conversion. (Und.) 
D)  Subcontrary. (T) 
E)  Contraposition. (Und.)

Question 18

The categorical proposition "Some admirers of Bertolt Brecht are not avid theater-goers" is an:

Accepted Answer

A)  E-type. 
B)  U-type. 
C)  I-type. 
D)  O-type. 
E)  A-type. 
A)  E-type. 
B)  U-type. 
C)  I-type. 
D)  O-type. 
E)  A-type.

Question 19

It is false that some four-sided triangles are commonplace figures. Therefore, some four-sided triangles are not commonplace figures.

Accepted Answer

A)  Valid, no fallacy. 
B)  Invalid, existential fallacy. 
C)  Invalid, illicit subcontrary. 
D)  Invalid, illicit contrary. 
E)  Invalid, illicit subalternation. 
A)  Valid, no fallacy. 
B)  Invalid, existential fallacy. 
C)  Invalid, illicit subcontrary. 
D)  Invalid, illicit contrary. 
E)  Invalid, illicit subalternation.

Question 20

Some non-A are non-B. (F) Some non-A are not non-B.

Accepted Answer

A)  Contraposition. (F) 
B)  Subalternation. (Und.) 
C)  Contradictory. (T) 
D)  Subalternation. (F) 
E)  Subcontrary. (T) 
A)  Contraposition. (F) 
B)  Subalternation. (Und.) 
C)  Contradictory. (T) 
D)  Subalternation. (F) 
E)  Subcontrary. (T)

Some poets are sensitive souls. Therefore, some poets are not insensitive souls.

It is false that all cowboys are romantic icons. Therefore, no cowboys are romantic icons.

All proponents of globalization are individuals unconcerned with world poverty. Therefore, all individuals concerned with world poverty are opponents of globalization.

It is false that some rare coins are worthless collectibles. Therefore, it is false that all rare coins are worthless collectibles.

No mint juleps are sour concoctions. Therefore, no sour concoctions are mint juleps.

Some crystal vases are not China teapots. Therefore, some China teapots are not crystal vases.

Given the categorical proposition "Some mathematicians are not topologists." If the quantity but not the quality is changed, the resulting proposition is:

It is false that all water sprites are charming nymphs. Therefore, some water sprites are not charming nymphs.

Not all parrots are colorful.

It is false that no high schools are institutions plagued by drunkenness. Therefore, it is false that some high schools are not institutions plagued by drunkenness.

It is false that some gothic cathedrals are not rich legacies. Therefore, some gothic cathedrals are rich legacies.

She sings whenever she is happy.

Some weekend getaways are not relaxing vacations. Therefore, some weekend getaways are relaxing vacations.

Some non-A are non-B. (F) Some B are A.

The categorical proposition "Some admirers of Bertolt Brecht are not avid theater-goers" is an:

It is false that some four-sided triangles are commonplace figures. Therefore, some four-sided triangles are not commonplace figures.

Some non-A are non-B. (F) Some non-A are not non-B.

Basic Concepts

Language: Meaning and Definition

Informal Fallacies

Categorical Syllogisms

Propositional Logic

Natural Deduction in Propositional Logic

Predicate Logic

Analogy and Legal and Moral Reasoning

Causality and Mills Methods

Probability

Statistical Reasoning

Hypotheticalscientific Reasoning

Science and Superstition

Filters

Exam 4: Categorical Propositions

Some poets are sensitive souls. Therefore, some poets are not insensitive souls.

It is false that all cowboys are romantic icons. Therefore, no cowboys are romantic icons.

All proponents of globalization are individuals unconcerned with world poverty. Therefore, all individuals concerned with world poverty are opponents of globalization.

It is false that some rare coins are worthless collectibles. Therefore, it is false that all rare coins are worthless collectibles.

No mint juleps are sour concoctions. Therefore, no sour concoctions are mint juleps.

Some crystal vases are not China teapots. Therefore, some China teapots are not crystal vases.

Given the categorical proposition "Some mathematicians are not topologists." If the quantity but not the quality is changed, the resulting proposition is:

It is false that all water sprites are charming nymphs. Therefore, some water sprites are not charming nymphs.

Not all parrots are colorful.

It is false that no high schools are institutions plagued by drunkenness. Therefore, it is false that some high schools are not institutions plagued by drunkenness.

It is false that some gothic cathedrals are not rich legacies. Therefore, some gothic cathedrals are rich legacies.

She sings whenever she is happy.

Some weekend getaways are not relaxing vacations. Therefore, some weekend getaways are relaxing vacations.

Some non-A are non-B. (F) Some B are A.

The categorical proposition "Some admirers of Bertolt Brecht are not avid theater-goers" is an:

It is false that some four-sided triangles are commonplace figures. Therefore, some four-sided triangles are not commonplace figures.

Some non-A are non-B. (F) Some non-A are not non-B.

Basic Concepts

Language: Meaning and Definition

Informal Fallacies

Categorical Syllogisms

Propositional Logic

Natural Deduction in Propositional Logic

Predicate Logic

Analogy and Legal and Moral Reasoning

Causality and Mills Methods

Probability

Statistical Reasoning

Hypotheticalscientific Reasoning

Science and Superstition

Filters