Logic Chapter 9

Can both A and E statements be true at the same time?

-No, both A and E statements can not be true at the same time.

Which other pair of statements are subcontrary to one another?

...

In the following chart, indicate, as in Figure 7-2, which two pairs of statements are contradictory which two are contrary, which two statements are subcontrary, and which two statements are subalternate: A I E O

A & E-Contraries A & I- Subalterns E & O-Subalterns I & O- Subcontraries A & O- Contradictories E & I-Contradictories

Which pair of statements comply with the Second Law of Opposition?

A and E statements comply with the Second Law of Opposition.

In the following chart, indicate, as in Figure 6-2, which two pairs of statements are contradictory and which two are contrary: A E I O

A and E-contrary A and O-contradictory E and I- contradictory

Which pairs of statements comply with the Fourth Law of Opposition?

A and I statements and E and O statements comply with the Fourth Law of Opposition.

Which two pairs of statements are affected by the First Law of Opposition?

A and O and E and I statements are affected by the First Law of Opposition.

Fill out the following chart: Affirmative Neg Universal Particular

Affirmative Neg Universal A I Particular E O

Fill out the following chart: Affirmative Neg. Universal Particular

Affirmative Neg. Universal A E Particular I O

42. Show the quality and quantity of the four logical statements by filling out the following chart: Affirmative Negative Universal Particular

Affirmative Negative Universal A E Particular I O

Change the quality of the statement: No logic problems are difficult.

All logic problems are difficult.

Negate the predicate in the statement: No logic problems are difficult.

All logic problems are difficult.

Obvert the following statement: No logic problems are difficult.

All logic problems are not difficult.

Obvert the following statement: No men are white.

All men are not white.

Change the quality of the statement: No men are white.

All men are white.

Negate the predicate in the statement: No men are white.

All men are white.

Are these two statements Contradictory or not: Some animals are amphibians and No animals are amphibians.

Contradictory

Are these two statements Contradictory or not: Some omelets are tasty and No omelets are tasty.

Contradictory

Are these two statements Contradictory or not: Some soldiers are not brave and All soldiers are brave.

Contradictory

Are these two statements Contradictory or not:Some tomatoes are not red and all tomatoes are red.

Contradictory

How are these two statements logically equivalent to each other: All logic problems are difficult and All non-difficult things are not logic problems.

Contrapositive

How are these two statements logically equivalent to each other: All men are white and All non-white things are not men.

Contrapositive

How are these two statements logically equivalent to each other: All men are white and All not-white people are non-men.

Contrapositive

How are these two statements logically equivalent to each other: Some logic problems are not difficult and Some non-difficult things are not logic problems.

Contrapositive

How are these two statements logically equivalent to each other: Some men are not white and Some non-white people are men.

Contrapositive

Are these two statements contrary or not: All logic problems are difficult and No logic problems are difficult.

Contrary

Are these two statements contrary or not: All men are white and No men are white.

Contrary

Are these two statements contrary or not: All wars are bloody and No wars are bloody.

Contrary

Are these two statements contrary or not: Michael Jordan is a good basketball player and Michael Jordan is not a good basketball player.

Contrary

Are these two statements contrary or not: No cars are fast and All cars are fast.

Contrary

Are these two statements contrary or not: No houses are well-built and All houses are well-built.

Contrary

Are these two statements contrary or not: No logic problems are difficult and All logic problems are difficult.

Contrary

Are these two statements contrary or not: No men are white and All men are white.

Contrary

How are these two statements logically equivalent to each other: No logic problems are difficult and No difficult things are logic problems.

Converse

How are these two statements logically equivalent to each other: Some logic problems are difficult and Some difficult things are logic problems.

Converse

How are these two statements logically equivalent to each other: Some men are white and Some white people are men.

Converse

True or False:The statement "Just do it" and the statement "All men are mortal" are subcontrary.

False, "Just do it" is not a proposition so it cannot be subcontrary.

True or False:The statement "Just do it" and the statement "All men are mortal" are contradictory.

False, "Just do it" is not a proposition.

True or False: A statement can be contraposed by converting it, obverting it, and then converting it again.

False, A statement can be contraposed by obverting it, converting it, and then obverting it again

True or False: Contrary statements cannot at the same time be false, but they can both be true.

False, Contrary statements cannot at the same time be true, but they can both be false.

True or False: The statement "All lobsters are angry" and the statement "No lobsters are not angry" are contrapositive.

False, The statement "All lobsters are angry" and the statement "All non-angry things are non-lobsters" are contrapositive.

True or False: The three ways statements can be converted into their logical equivalents are by obversion, conversion, and subalternation.

False, The three ways statements can be converted into their logical equivalents are by obversion, conversion, and contraposition.

True or False:Subalternate statements cannot at the same time be false, but they can both be true.

False, subalternate statements can both be false at the same time, or they can both be true at the same time.

True or False:The A statement and the I statement differ in quality and quantity.

False, the A statement and the I statement differ in quantity but are the same in quality.

True or False:The quality of the statement "All S is P" is universal.

False, the quantity of the statement "All S is P" is universal.

True or False: The statements "All S is P" and "No S is P" can both be true at the same time.

False, the statements "All S is P" and "No S is P" cannot both be true at the same time.

True or False: Two statements are contradictory if they differ from each other in quality, but are the same in quantity.

False, two statements are contradictory if they differ in both quality and quantity.

Write five pairs of contradictory statements that are not in the book.

Five pairs of contradictory statements that are not in the book are: -All cats are black and Some cats are not black -No cats are black and Some cats are black -All dogs are brown and Some dogs are not brown -No dogs are brown and Some dogs are brown -All birds are red and Some birds are not red

Write five pairs of contrary statements that are not in the book.

Five pairs of contrary statements that are not in the book are: -All cats are black and No cats are black -All dogs are brown and No dogs are brown -All birds are red and No birds are red -All pens are pink and No pens are pink -All pencils are yellow and No pencils are yellow

Write five pairs of subalternate statements that are not in the book.

Five pairs of subalternate statements that are not in the book are All dogs are black and some dogs are black, No dogs are black and some dogs are not black, All rings are gold and some rings are gold, No rings are gold and some rings are not gold, All birds are red and some birds are red.

Write five pairs of subcontrary statements that are not in the book.

Five pairs of subcontrary that are not in the book are Some dogs are black and Some dogs are not black, Some rings are gold and some rings are not gold, some birds are red and some birds are not red, Some cats are white and some cats are not white, and some fish are orange and some fish are not orange.

Which pair of statements complies with the Third Law of Opposition?

I and O statements comply with the Third Law of Opposition.

What do we mean in logic when we speak of 'opposition'?

In logic when we speak of "opposition we mean the relationship which we call 'opposite'. If we say something is the opposite of another thing, we are saying the two things have a relationship of oppodition.

What are we discussing in this chapter?

In this chapter, we are discussing the different ways in which propositions are equivalent.

Define 'judgment'.

Judgment is the mental act whose verbal expression is what we call a proposition.

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Not immortal

Mortal

Contrapose the following statement: No cars are fast.

N/A

Contrapose the following statement: No guns are loud.

N/A

Contrapose the following statement: No houses are well-built.

N/A

Contrapose the following statement: No logic problems are difficult.

N/A

Contrapose the following statement: No men are saved.

N/A

Contrapose the following statement: No men are white.

N/A

Contrapose the following statement: Some animals are amphibian.

N/A

Contrapose the following statement: Some logic problems are difficult.

N/A

Contrapose the following statement: Some men are sinners.

N/A

Contrapose the following statement: Some men are white.

N/A

Contrapose the following statement: Some omelets are tasty.

N/A

Contrapose the following statement: Some rocks are crystals.

N/A

Convert the following statement: All logic problems are difficult.

N/A

Convert the following statement: All men are white.

N/A

Convert the following statement: Some logic problems are not difficult.

N/A

Convert the following statement: Some men are not white.

N/A

Are these statements contradictory to each other: All logic problems are difficult and Some logic problems are difficult.

No

Are these statements contradictory to each other:All logic problems are difficult and No logic problems are difficult.

No

Are these statements contradictory to each other:All men are white and Some men are white.

No

Are these statements contradictory to each other:All men are white and no men are white.

No

Are these statements contradictory to each other:No logic problems are difficult and All logic problems are difficult.

No

Are these statements contradictory to each other:No logic problems are difficult and Some logic problems are not difficult.

No

Are these statements contradictory to each other:No men are white and All men are white.

No

Are these statements contradictory to each other:No men are white and Some men are not white.

No

Are these statements contradictory to each other:Some logic problems are difficult and Some logic problems are not difficult.

No

Are these statements contradictory to each other:Some men are white and Some men are not white.

No

Convert the following statement: No logic problems are difficult.

No difficult things are logic problems.

Change the quality of the statement: All logic problems are difficult. No logic problems are difficult.

No logic problems are difficult.

Negate the predicate in the statement: All logic problems are difficult.

No logic problems are difficult.

Obvert the following statement: All logic problems are difficult.

No logic problems are not difficult.

Obvert the following statement: All men are white.

No logic problems are not difficult.

Change the quality of the statement: All men are white.

No men are white.

Negate the predicate in the statement: All men are white.

No men are white.

Convert the following statement: No men are white.

No white things are men.

Can both A and O statements be false at the same time?

No, both A and O statements can not be false at the same time.

Can both A and O statements be true at the same time?

No, both A and O statements can not be true at the same time.

Can both A and O statements be true at the same time?

No, both A and O statements cannot be true at the same time.

Can both E and I statements be false at the same time?

No, both E and I statements can not be false at the same time.

Can both E and I statements be true at the same time?

No, both E and I statements can not be true at the same time.

Can both E and I statements be false at the same time?

No, both E and I statements cannot be false at the same time.

Can both E and I statements be true at the same time?

No, both E and I statements cannot be false at the same time.

Can both I and O statements can both be false at the same time?

No, both I and O statements can not both be false at the same time.

Are there any other pairs of statements that are contrary to one another? If so, indicate which they are.

No, there is no other pairs of statements that are contrary to one another.

Can you negate a predicate-term like 'large' by replacing it with 'small'? If not, explain why.

No, you cannot negate a predicate-term like 'large' by replacing it with 'small' because the negation of the thing to which the predicate refers may not be either large or small, but somewhere in between.

Are the two statements subcontrary or not: All machines are loud and Some machines are loud.

Not

Are the two statements subcontrary or not: All storms are violent and Some storms are violent.

Not

Are the two statements subcontrary or not: All wars are bloody and No wars are bloody.

Not

Are the two statements subcontrary or not: No cars are fast and All cars are fast.

Not

Are the two statements subcontrary or not: No guns are loud and Some guns are not loud.

Not

Are the two statements subcontrary or not: No houses are well-built and All houses are well-built.

Not

Are the two statements subcontrary or not: No men are saved and Some men are not saved.

Not

Are the two statements subcontrary or not: Some animals are amphibian and No animals are amphibian.

Not

Are the two statements subcontrary or not: Some omelets are tasty and No omelets are tasty.

Not

Are the two statements subcontrary or not: Some soldiers are not brave and All soldiers are brave.

Not

Are the two statements subcontrary or not: Some tomatoes are not red and All tomatoes are red.

Not

Are the two statements subcontrary or not: Tim Couch is a good quarterback. X Tim Couch is not a good quarterback.

Not

Are these two statements Contradictory or not: All machines are loud and Some machines are loud.

Not

Are these two statements Contradictory or not: All storms are violent and Some storms are violent.

Not

Are these two statements Contradictory or not: All wars are bloody and no wars are bloody.

Not

Are these two statements Contradictory or not: Michael Jordan is a good basketball player and Michael Jordan is not a good basketball player.

Not

Are these two statements Contradictory or not: No cars are fast and All cars are fast..

Not

Are these two statements Contradictory or not: No guns are loud and Some guns are not loud.

Not

Are these two statements Contradictory or not: No houses are well-built and all houses are well-built.

Not

Are these two statements Contradictory or not: No men are saved and Some men are not saved.

Not

Are these two statements Contradictory or not: Some men are sinners and Some men are not sinners.

Not

Are these two statements Contradictory or not: Some rocks are crystals and Some rocks are not crystals.

Not

Are these two statements contrary or not: All logic problems are difficult and Some logic problems are difficult.

Not

Are these two statements contrary or not: All machines are loud and Some machines are loud.

Not

Are these two statements contrary or not: All men are white and Some men are white.

Not

Are these two statements contrary or not: All storms are violent and Some storms are violent.

Not

Are these two statements contrary or not: No logic problems are difficult and Some logic problems are not difficult.

Not

Are these two statements contrary or not: No men are saved and Some men are not saved.

Not

Are these two statements contrary or not: Some animals are amphibians and No animals are amphibians.

Not

Are these two statements contrary or not: Some logic problems are difficult and No logic problems are difficult.

Not

Are these two statements contrary or not: Some logic problems are difficult and Some logic problems are not difficult .

Not

Are these two statements contrary or not: Some logic problems are not difficult and All logic problems are difficult.

Not

Are these two statements contrary or not: Some men are sinners and Some men are not sinners.

Not

Are these two statements contrary or not: Some men are white and No men are white.

Not

Are these two statements contrary or not: Some men are white and Some men are not white.

Not

Are these two statements contrary or not: Some rocks are crystals and Some rocks are not crystals.

Not

Are these two statements contrary or not: Some soldiers are not brave and All soldiers are brave.

Not

Are these two statements contrary or not: Some tomatoes are not red and All tomatoes are red.

Not

Are these two statements contrary or not:No guns are loud and Some guns are not loud.

Not

Are these two statements contrary or not:No men are white and Some men are not white.

Not

Are these two statements contrary or not:Some men are not white and All men are white.

Not

Are these two statements contrary or not:Some omelets are tasty and No omelets are tasty.

Not

Are these two statements subalternate or not: All logic problems are difficult and No logic problems are difficult.

Not

Are these two statements subalternate or not: All men are white and No men are white.

Not

Are these two statements subalternate or not: All wars are bloody and No wars are bloody.

Not

Are these two statements subalternate or not: Michael Jordan is a good basketball player and Michael Jordan is not a good basketball player.

Not

Are these two statements subalternate or not: No cars are fast and All cars are fast.

Not

Are these two statements subalternate or not: No houses are well-built and All houses are well-built.

Not

Are these two statements subalternate or not: No logic problems are difficult and All logic problems are difficult.

Not

Are these two statements subalternate or not: No men are white and All men are white.

Not

Are these two statements subalternate or not: Some animals are amphibian and No animals are amphibian.

Not

Are these two statements subalternate or not: Some logic problems are difficult and No logic problems are difficult.

Not

Are these two statements subalternate or not: Some logic problems are difficult and Some logic problems are not difficult.

Not

Are these two statements subalternate or not: Some logic problems are not difficult and All logic problems are difficult.

Not

Are these two statements subalternate or not: Some men are not white and All men are white.

Not

Are these two statements subalternate or not: Some men are sinners and Some men are not sinners.

Not

Are these two statements subalternate or not: Some men are white and No men are white.

Not

Are these two statements subalternate or not: Some omelets are tasty and No omelets are tasty.

Not

Are these two statements subalternate or not: Some rocks are crystals and Some rocks are not crystals.

Not

Are these two statements subalternate or not: Some soldiers are not brave and All soldiers are brave.

Not

Are these two statements subalternate or not: Some tomatoes are not red and All tomatoes are red.

Not

Are these two statements subalternate or not:Some men are white and Some men are not white.

Not

Are these two statements subcontrary or not: All logic problems are difficult and No logic problems are difficult.

Not

Are these two statements subcontrary or not: All logic problems are difficult and Some logic problems are difficult.

Not

Are these two statements subcontrary or not: All men are white and No men are white.

Not

Are these two statements subcontrary or not: All men are white and Some men are white.

Not

Are these two statements subcontrary or not: No logic problems are difficult and All logic problems are difficult.

Not

Are these two statements subcontrary or not: No logic problems are difficult and Some logic problems are not difficult.

Not

Are these two statements subcontrary or not: No men are white and All men are white.

Not

Are these two statements subcontrary or not: No men are white and Some men are not white.

Not

Are these two statements subcontrary or not: Some logic problems are difficult and No logic problems are difficult.

Not

Are these two statements subcontrary or not: Some logic problems are not difficult and All logic problems are difficult.

Not

Are these two statements subcontrary or not: Some men are not white and All men are white.

Not

Are these two statements subcontrary or not: Some men are white and No men are white.

Not

How are these two statements logically equivalent to each other: All logic problems are difficult and No logic problems are not difficult.

Obverse

How are these two statements logically equivalent to each other: No men are white and All men are non-white.

Obverse

How are these two statements logically equivalent to each other: Some logic problems are difficult and Some logic problems are not non-difficult.

Obverse

How are these two statements logically equivalent to each other: Some men are white and Some men are not non-white.

Obverse

With which of the four categorical statements can obversion be used?

Obversion can be used on all four of the categorical statements.

Which of the four kinds of categorical statements can be contraposed?

Only A and O statements can be contraposed.

Tell the quality and quantity of the A statement.

Quality-affirmative Quantity- universal

Tell the quality and quantity of the A statement.

Quality-affirmative Quantity-universal

Tell the quality and quantity of the O statement.

Quality-negative Quantity-particular

Tell the quality and quantity of the E statement.

Quality-negative Quantity-universal

Partially convert the following A statement: All lobsters are angry.

Some angry things are lobsters.

Partially convert the following A statement: All Americans are brave.

Some brave things are Americans.

Convert the following statement: Some logic problems are difficult.

Some difficult things are logic problems.

Partially convert the following A statement: All horses are fast.

Some fast things are horses.

Partially convert the following A statement: All geraniums are irrational.

Some irrational things are geraniums.

Change the quality of the statement: Some logic problems are not difficult.

Some logic problems are difficult.

Negate the predicate in the statement: Some logic problems are not difficult.

Some logic problems are difficult.

Change the quality of the statement: Some logic problems are difficult.

Some logic problems are not difficult.

Negate the predicate in the statement: Some logic problems are difficult.

Some logic problems are not difficult.

Obvert the following statement: Some logic problems are not difficult.

Some logic problems are not difficult.

Obvert the following statement: Some logic problems are difficult.

Some logic problems are not non-difficult.

Partially convert the following A statement: All babies are loud.

Some loud things are babies.

Obvert the following statement: Some men are white.

Some men are not non-white.

Change the quality of the statement:Some men are white.

Some men are not white.

Negate the predicate in the statement: Some men are white.

Some men are not white.

Obvert the following statement: Some men are not white.

Some men are not white.

Change the quality of the statement: Some men are not white.

Some men are white.

Negate the predicate in the statement: Some men are not white.

Some men are white.

Partially convert the following A statement: All oysters are quiet.

Some quiet things are oysters.

Partially convert the following A statement: All pigs are smelly.

Some smelly things are pigs.

Partially convert the following A statement: All mammals breathe oxygen.

Some things that breathe oxygen are mammals.

Convert the following statement: Some men are white.

Some white things are men.

Are statements in which the subject-term is the name of a certain individual universal or particular? Explain.

Statements in which the subject-term is the name of a certain individual is universal because it applies to all of the subject-class which is the one person.

Contrapose the following statement: Michael Jordan is a good basketball player.

Step 1: No Michael Jordan is not a good basketball player. Step 2: No non-good basketball players are Michael Jordan. Step 3: All not good basketball players are not Michael Jordan.

Show each step in the process of contraposition for the following statement: All lobsters are angry.

Step 1: No lobsters are non-angry. Step 2: No non-angry things are lobsters. Step 3: All non-angry things are non-lobsters.

Contrapose the following statement: All logic problems are difficult.

Step 1: No logic problems are non-difficult. Step 2: No non-difficult things are logic problems. Step 3: All non-difficult things are non-logic problems.

Contrapose the following statement: All machines are loud.

Step 1: No machines are non-loud. Step 2: No non-loud things are machines. Step 3: All non-loud things are non-machines.

Show each step in the process of contraposition for the following statement: All men are animals.

Step 1: No men are non-animals. Step 2: No non-animals are men. Step 3: All non-animals are non-men.

Show each step in the process of contraposition for the following statement: All men are mortal.

Step 1: No men are non-mortal. Step 2: No non-mortals are men. Step 3: All non-mortals are non-men.

Contrapose the following statement: All men are white.

Step 1: No men are non-white. Step 2: No non-white things are men. Step 3: All not-white things are non-men.

Show each step in the process of contraposition for the following statement: All oysters are quiet.

Step 1: No oysters are non-quiet. Step 2: No non-quiet things are oysters. Step 3: All non-quiet things are non-oysters.

Show each step in the process of contraposition for the following statement: All pigs are smelly.

Step 1: No pigs are non-smelly. Step 2: No non-smelly things are pigs. Step 3: All non-smelly things are non-pigs.

Contrapose the following statement: All storms are violent.

Step 1: No storms are non-violent. Step 2: No non-violent things are storms. Step 3: All non-violent things are non-storms.

Contrapose the following statement: All wars are bloody.

Step 1: No wars are non-bloody. Step 2: No non-bloody things are wars. Step 3: All non-bloody things are non-wars.

Contrapose the following statement: Some logic problems are not difficult.

Step 1: Some logic problems are difficult. Step 2: Some non-difficult things are non-logic problems. Step 3: Some not-difficult things are logic problems.

Contrapose the following statement: Some men are not white.

Step 1: Some men are not white. Step 2: Some non-white things are men. Step 3:Some white things are not men.

Contrapose the following statement: Some soldiers are not brave.

Step 1: Some soldiers are brave. Step 2: Some non-brave things are not soldiers. Step 3: Some non-brave things are soldiers.

Contrapose the following statement: Some tomatoes are not red.

Step 1: Some tomatoes are red. Step 2: Some non-red things are non-tomatoes. Step 3: Some non-red things are tomatoes.

Are these two statements subalternate or not: All logic problems are difficult and Some logic problems are difficult.

Subalternate

Are these two statements subalternate or not: All machines are loud and Some machines are loud.

Subalternate

Are these two statements subalternate or not: All men are white and Some men are white.

Subalternate

Are these two statements subalternate or not: All storms are violent and Some storms are violent.

Subalternate

Are these two statements subalternate or not: No guns are loud and Some guns are not loud.

Subalternate

Are these two statements subalternate or not: No men are saved and Some men are not saved.

Subalternate

Are these two statements subalternate or not:No logic problems are difficult and Some logic problems are not difficult.

Subalternate

Are these two statements subalternate or not:No men are white and Some men are not white.

Subalternate

Are the two statements subcontrary or not: Some men are sinners and Some men are not sinners.

Subcontrary

Are the two statements subcontrary or not: Some rocks are crystals and Some rocks are not crystals.

Subcontrary

Are these two statements subcontrary or not: Some logic problems are difficult and Some logic problems are not difficult.

Subcontrary

Are these two statements subcontrary or not: Some men are white and Some men are not white.

Subcontrary

Explain why the A statement "All S is P" and the E statement "No S is P" are not contradictory.

The A statement "All S is P" and the E statement "No S is P" are not contradictory because even though they differ in quality, they are both universal.

Explain why the A statement "All S is P" and the E statement "No S is P" are not subalternate.

The A statement "All S is P" and the E statement "No S is P" are not subalternate because they differ in quality but are the same in quantity and for two statements to be subalternate they must have the same quality, but differ in quantity.

Explain why the A statement "All S is P" and the E statement "No S is P" are not subcontrary.

The A statement "All S is P" and the E statement "No S is P" are not subcontrary because subcontrary statements have to be particular and A and E statements are universal.

Explain why the A statement "All S is P" and the O statement "Some S is not P" are not contrary.

The A statement "All S is P" and the O statement "Some S is not P" are not contrary because they differ in quality and quantity.

Which other pair of statements is contradictory to one another?

The E and I statements are contradictory to one another.

What is the First Law of Opposition?

The First Law of Opposition is Contradictory statements cannot at the same time be true nor at the same time be false.

What is the First Law of Opposition?

The First Law of Opposition is contradictories cannot at the same time be true nor at the same time be false.

What is the Fourth Law of Opposition?

The Fourth Law of Opposition is subalterns may both be true or both be false. If the particular is false, the universal is false; if the universal is true, then the particular is true; otherwise, their status is indeterminate.

Explain why the I statement "Some S is P" and the E statement "No S is P" are not contrary.

The I statement "Some S is P" and the E statement "No S is P" are not contrary because they differ in quality

Explain why the I statement "Some S is P" and the O statement "Some S is not P" are not subalternate.

The I statement "Some S is P" and the O statement "Some S is not P" are not subalternate because they differ in quality but are the same in quantity and for two statements to be subalternate they must have the same quality, but differ in quantity.

Is the I statement subcontrary to the O statement? If so, explain why; if not, explain why not.

The I statement is subcontrary to the O statement because they are both particular but differ in quality.

What is the Rule of Contradiction?

The Rule of Contradiction is Contradictory statements are statements that differ in both quality and quantity.

Express the Rule of Contradiction.

The Rule of Contradiction is contradictory statements are statements that differ in both in quality and quantity.

Express the Rule of Contraries.

The Rule of Contraries is two statements are contrary to one another if they are both universal but differ in quality.

What is the Rule of Contraries?

The Rule of Contraries is two statements are contrary to one another if they are both universals but differ in quality.

What is the Rule of Subalternates?

The Rule of Subalterns is two statements are subalternate if they have the same quality but differ in quantity.

Express the Rule of Subalterns.

The Rule of Subalterns is two statements are subalternate if they have the same quality, but differ in quantity.

Express the Rule of Subcontraries.

The Rule of Subcontraries is two statements are subcontrary if they are both particular statements that differ in quality.

What is the Rule of Subcontraries?

The Rule of Subcontraries is two statements are subcontrary if they are both particular statements that differ in quality.

What is the Second Law of Opposition?

The Second Law of Opposition is Contraries cannot at the same time both be true, but can at the same time both be false.

What is the Second Law of Opposition?

The Second Law of Opposition is contraries cannot at the same time both be true, but can at the same time both be false.

What is the Third Law of Opposition?

The Third Law of Opposition is subcontraries may at the same time both be true, but cannot at the same time both be false.

Which of the categorical statements (A, I, E, and O) can be converted?

The categorical statements, E and I can be obverted.

What are the four basic statement with which logic deals?(Use the letters S and P to show their form.)

The four basic statements with which logic deals are: -All S is P -Some S is P -No S is P -Some S is not P

What are the four elements of a proposition?

The four elements of a proposition are the subject-term, the predicate-term, the quantifier, and the copula.

What are the four ways A, I, E, and O statements can be related to one another in opposition?

The four ways A, I, E, and O statements can be related to one another in opposition is contradictory, contrary, subcontrary, and subalternate.

What are the four ways A, I, E, and O statements can be related to one another in opposition?

The four ways that A, I, E, and O statements can be related to one another in opposition are to be contradictory, contrary, subcontrary, and subalternate.

What are the four ways you can handle the double-negated predicate in an I statement?

The four ways you can handle the double-negated predicate in an I statement are: 1.Simply place two 'not's at the beginning of the predicate-term. 2.Make the second 'not' a 'non' and attach it to the predicate word with a dash. 3.Place an 'im', 'un', 'in', or an 'ir' at the beginning of the predicate-term 4.Apply the rule of double negation.

What phrase do we use to indicate that two statements are logically the same?

The phrase that we use to indicate that two statements are logically the same is logically equivalent.

Tell the quality and quantity of the A statement.

The quality of the A statement is affirmative. The quantity of the A statement is universal.

Tell the quality and quantity of the I statement.

The quality of the I statement is affirmative. The quality of the I statement is particular.

Tell the quality and quantity of the I statement.

The quality of the I statement is affirmative. The quantity of the I statement is universal.

Tell the quality and quantity of the O statement.

The quality of the O statement is negative. The quality of the O statement is particular.

True or False:The A statement and the E statement are not contradictory because, although they differ in quality, they do not differ in quantity.

True

True or False:The A statement and the E statement are not subcontrary because, although they differ in quality, they are both universal.

True

True or False:The quantity of the statement "Some S is P" is particular.

True

True or False:The statements "All S is P" and "Some S is P" can both be false at the same time.

True

True or False:The statements "All S is P" and "Some S is P" can both be true at the same time.

True

True or False:The statements "All football players are big" and "Some football players are big" are subalternate.

True

True or False:Two statements are subcontrary if they differ from each other in quality, and are both particular.

True

Does the A statement contradict the O statement? If so, explain why; if not, explain why not.

Yes, the A statement contradicts the O statement because they differ in both quality and quantity.

Is the A statement contrary to the E statement? If so, explain why; if not, explain why not.

Yes, the A statement is contrary to the E statement because even though they differ in quality, they are both universal.

Is the A statement subalternate to the I statement? If so, explain why; if not, explain why not.

Yes, the A statement is subalternate to the I statement because they have the same quality (affirmative) but differ in quantity( A-universal, I-particular).

Are there any other pairs of statements that are subalternate to one another? If so, indicate which they are.

Yes, there is one other pair of statements that are subalternate to one another and they are the E and O statements.

How do you change the quality of a statement?

You change the quality of a statement by changing an affirmative statement to be negative and changing a negative statement to be affirmative.

How do you convert a statement?

You convert a statement by simply interchanging the subject and the predicate.

How do you determine whether a proposition is in logical form?

You determine whether a propositon is in logical form by checking it has a subject-term, a predicate-term, a copula, and a quantifier.

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Not non-animal

animal

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Not non-illogical

illogical

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Not non-immortal

immortal

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Not illogical

logical

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Not not non-animal

non-animal

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Illogical

not logical

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Immortal

not mortal

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Non-white

not non non-white

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Animal

not non-animal

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Logical

not non-logical

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Mortal

not non-mortal

Use the rule of double negation to convert the following terms into another term that is logically equivalent: White

not non-white

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Non-animal

not not non-animal

Can both E and O statements be false at the same time?

Yes, both E and O statements can be false at the same time.

Can both E and O statements be true at the same time?

Yes, both E and O statements can be true at the same time.

Can both I and O statements be true at the same time?

Yes, both I and O statements can both be true at the same time.

True or False: Conversion can be performed on O statements.

True

True or False: Obversion can be performed on all four kinds of statements.

True

True or False: One of the ways to phrase the predicate when obverting an I statement is to use the rule of double negation.

True

True or False: The A statement and the O statement differ in quality and quantity.

True

True or False: The quantity of the statement "Some S is P" is particular.

True

True or False: The statements "All S is P" and "No S is P" can both be false at the same time.

True

True or False: The statements "All football players are big" and "No football players are big" are contrary.

True

True or False: There are only two steps involved in obversion.

True

Define 'proposition'.

A proposition is a sentence or statement which expresses truth or falsity.

What is the rule of double negation?

The rule of double negation says that a term which is not negated is equivalent to a term that is negated twice (and vice-versa).

What are the three ways in which statements can be converted into their logical equivalents?

The three ways in which statements can be converted into their logical equivalents are obversion, conversion, and contraposition.

Give the three-step method for contraposing a statement?

The three-step method for contraposing a statement are: 1. Obvert the statement. 2. Convert the statement. 3. Obvert the statement again.

What are the two fundamental characteristics of categorical propositions?

The two fundamental characteristics of categorical propositions are quality and quantity.

What are the two kinds of relationships statements can have to one another?

The two relationships statements can have to another are opposition and equivalence.

Give the two-step method for obverting a statement.

The two-step method for obverting a statement is: 1.Change the quality of the sentence. 2.Negate the predicate.

What do we call the verbal expression of a judgment?

The verbal expression of a judgment is the proposition.

With which two of these is this chapter concerned?

This chapter is concerned with subcontrary and subalternate statements.

How does this happen?

This happens because you change the quality from affirmative to negative in step 1 and then you negate the predicate in step 2.

How do you negate the predicate of a statement?

To negate the proposition, you simply add a not in front of it.

What does it mean to say that a proposition is in 'proper logical form'?

To say that a proposition is in 'proper logical form' means that it has the four elements of a proposition.

When should we apply the rule of double negation and when should we not apply it?

We should apply the rule of double negation when it is necessary to. We should not apply it when it sounds awkward.

When an O statement has been obverted, how many negations are contained in the predicate (before applying the rule of double negation?

When an O statement has been obverted, there are 3 negations contained in the predicate.

When the O statement has been obverted and the rule of double negation applied, to what is the statement similar?

When the O statement has been obverted and the rule of double negation applied, it is similar to the original statement.

What happens to the predicate in I statements when they are obverted?

When they are obverted, the predicate in I statements is negated twice.

What do you have to be careful about when using the third of these methods (negating by the use of 'im', 'un', 'in', or 'ir')?

When using the third of these methods (negating by use of 'im', 'un', 'in', or 'ir') you have to be careful of words that begin with 'im', 'un', 'in', or 'ir' because those are not the actual negation of the original word.

What are we doing when we oppose propositions?

When we oppose propositions, we are saying the two things affirm and deny the same subject and predicate but differ in quality and quantity.

Are these statements contradictory to each other:Some logic problems are difficult and No logic problems are difficult.

Yes

Are these statements contradictory to each other:Some logic problems are not difficult and All logic problems are difficult.

Yes

Are these statements contradictory to each other:Some men are not white and All men are white.

Yes

Are these statements contradictory to each other:Some men are white and No men are white.

Yes

Is there any way in which the A statement can be converted? If so, how?

Yes, A statements can be converted through partial conversion, which is done by interchanging the subject and the predicate and changing the statement from universal to particular.

Can both A and E statements be false at the same time?

Yes, both A and E statements can be false at the same time.

Can both A and I statements be false at the same time?

Yes, both A and I statements can be false at the same time.

Can both A and I statements be true at the same time?

Yes, both A and I statements can be true at the same time.

Use the rule of double negation to convert the following terms into another term that is logically equivalent: Not non-white

white

Think of five statements and contrapose them.

•All bats are blind.-All non-blind things are non-bats. •Some days are not long.-Some not-long things are days. •All chairs are white.-All non-white things are non-chairs. •Some dresses are not pretty.-Some non-pretty things are dresses. •All dressers are navy.-All non-navy things are non-dressers.

Think of five of your own statements and obvert them.

•All shoes are tan.-No shoes are not tan. •Some fish are orange.-Some fish are not non-orange. •No cats are friendly.-All cats are not friendly. •Some dogs are not cute. - Some dogs are not cute. •All turtles are green.-No turtles are not green.

Think of five our your own statements and convert them.

•No dolphins are purple.-No purple things are dolphins. •Some men are pink.-No pink things are men. •No lobsters are red.-No red things are lobsters. •Some walks are long.-Some long things are walks. •No snow days are bad.-No bad things are snow days.