Exercises on Universal Syllogisms

1. What can you conclude from the following premises: "All Critical Thinking classes are full" and "John found a class that wasn't full."

Not all Critical Thinking classes are full.

John didn't find all the classes.

John found a class that wasn't Critical Thinking.

All Critical Thinking classes were not found.

2. Which of the following major premises forms a valid argument with the minor premise, "Sumerians invented the first written language," and the conclusion, "Sumerians created the modern world."

"The inventors of written language created the modern world."

"The Sumerians created modern writing."

"Written language is the foundation of the modern world."

The argument is invalid.

3. A line in a famous poem reads, "But only God can make a tree." On that basis, Joyce concluded that the lemon tree in his garden was made by God. Which of the following best describes Joyce's argument?

God is tree maker.

Lemon is tree.

Therefore, God is lemon maker.

God is tree maker.

Lemon is tree.

Therefore, invalid argument.

All trees are God-made.

Lemon is tree.

Therefore, lemon is God-made.

All trees are God-made.

Lemon is tree.

Therefore, invalid argument.

4. Consider the following chain argument: "All libraries are quiet. Only quiet places are restful. The places where I like to study are restful." What can you conclude from the minor premise, "My bedroom is a place where I like to study"?

My bedroom is restful, quiet, and a library.

My bedroom is restful and quiet.

Libraries are restful and my bedroom is quiet.

Libraries and my bedroom are places I like to study.

1. What can you conclude from the following premises: "All Critical Thinking classes are full" and "John found a class that wasn't full." You answered:

John found a class that wasn't Critical Thinking.

Correct!

The argument would be as follows:

All X are Y. No Z is Y. Therefore, no Z is X.

--or--

All CT classes are full. No John's class is full. Therefore, no John's class is CT.

2. Which of the following major premises forms a valid argument with the minor premise, "Sumerians invented the first written language," and the conclusion, "Sumerians created the modern world." You answered:

"The inventors of written language created the modern world."

Correct!

The argument would be as follows:

All X are Y. Z is X. Therefore, Z is Y.

--or--

Inventors are world creators. Sumerians are inventors. Therefore, Sumerians are world creators.

3. A line in a famous poem reads, "But only God can make a tree." On that basis, Joyce concluded that the lemon tree in his garden was made by God. Which of the following best describes Joyce's argument? You answered:

All trees are God-made.

Lemon is tree.

Therefore, lemon is God-made.

Correct!

The problem here is how to restate "Only God can make a tree." Because "Only A is B" is equivalent to "All B is A," we can convert it to "All trees are God-made."

4. Consider the following chain argument: "All libraries are quiet. Only quiet places are restful. The places where I like to study are restful." What can you conclude from the minor premise, "My bedroom is a place where I like to study"? You answered:

My bedroom is restful and quiet.

Correct!

When restated, the three premises in the chain are as follows:

1. All libraries are quiet places. 2. All restful places are quiet places. 3. My study places are restful places.

--or--

1. All A are B. 2. All C are B 3. All D are C

The first two premises do not form a valid chain, since affirming A or C produces a conclusion, B, which cannot be used as the minor premise in a valid argument with the other claim. Therefore, only premises 2 and 3 form the chain; affirming that E ("my bedroom") is D ("study place"), leads to the conclusion that E is also C ("restful place") and B ("quiet place").

1. What can you conclude from the following premises: "All Critical Thinking classes are full" and "John found a class that wasn't full." You answered:

Not all Critical Thinking classes are full.

Valid form: All X is Y No Z is Y. Therefore, no Z is X.

--but--

Your answer: All CT classes are full No John's class is full. Therefore, no all CT classes are full.

Even ignoring that added "all" in the conclusion, "CT classes" can't be Z in the conclusion and X in the major premise. Try again.

1. What can you conclude from the following premises: "All Critical Thinking classes are full" and "John found a class that wasn't full." You answered:

John didn't find all the classes.

Valid form: All X is Y No Z is Y. Therefore, no Z is X.

--but--

Your answer: All CT classes are full No John's class is full. Therefore, no all CT classes are found by John.

Even ignoring that added "all" in the conclusion, "CT classes" can't be Z in the conclusion and X in the major premise. Try again.

1. What can you conclude from the following premises: "All Critical Thinking classes are full" and "John found a class that wasn't full." You answered:

All Critical Thinking classes were not found.

Valid form: All X is Y No Z is Y. Therefore, no Z is X.

--but--

Your answer: All CT classes are full No John's class is full. Therefore, no all CT classes are found.

Even ignoring that added "all" in the conclusion, "CT classes" can't be Z in the conclusion and X in the major premise. Try again.

2. Which of the following major premises forms a valid argument with the minor premise, "Sumerians invented the first written language," and the conclusion, "Sumerians created the modern world." You answered:

"The Sumerians created modern writing."

The paradigm is: All X are Y. Z is X. Therefore, Z is Y.

--But--

You argued: Sumerians are writing creators Sumerians are writing inventors. Therefore, Sumerians are world creators.

Try again!

2. Which of the following major premises forms a valid argument with the minor premise, "Sumerians invented the first written language," and the conclusion, "Sumerians created the modern world."

"Written language is the foundation of the modern world."

The paradigm is: All X are Y. Z is X. Therefore, Z is Y.

--But--

You argued: Writing is foundation Sumerians are writing inventors. Therefore, Sumerians are world creators.

Try again!

2. Which of the following major premises forms a valid argument with the minor premise, "Sumerians invented the first written language," and the conclusion, "Sumerians created the modern world."

The argument is invalid.

The paradigm is: All X are Y. Z is X. Therefore, Z is Y.

--But--

You argued: [No premise possible] Sumerians are writing inventors. Therefore, Sumerians are world creators.

But there is a possible premise to make this argument valid. Try again!

3. A line in a famous poem reads, "But only God can make a tree." On that basis, Joyce concluded that the lemon tree in his garden was made by God. Which of the following best describes Joyce's argument? You answered:

God is tree maker.

Lemon is tree.

Therefore, God is lemon maker.

The problem here is how to restate "Only God can make a tree." Remember that "Only A is B" is equivalent to "All B is A."

3. A line in a famous poem reads, "But only God can make a tree." On that basis, Joyce concluded that the lemon tree in his garden was made by God. Which of the following best describes Joyce's argument? You answred:

God is tree maker.

Lemon is tree.

Therefore, invalid argument.

The problem here is how to restate "Only God can make a tree." Because "Only A is B" is equivalent to "All B is A."

3. A line in a famous poem reads, "But only God can make a tree." On that basis, Joyce concluded that the lemon tree in his garden was made by God. Which of the following best describes Joyce's argument? You answered:

All trees are God-made.

Lemon is tree.

Therefore, invalid argument.

The problem here is how to restate "Only God can make a tree." Because "Only A is B" is equivalent to "All B is A."

4. Consider the following chain argument: "All libraries are quiet. Only quiet places are restful. The places where I like to study are restful." What can you conclude from the minor premise, "My bedroom is a place where I like to study"? you answered:

Libraries and my bedroom are places I like to study.

When restated, the three premises in the chain are as follows:

1. All libraries are quiet places. 2. All restful places are quiet places. 3. My study places are restful places.

--or--

1. All A are B. 2. All C are B 3. All D are C

The first two premises do not form a valid chain, since affirming A or C produces a conclusion, B, which cannot be used as the minor premise in a valid argument with the other claim. Therefore, only premises 2 and 3 form the chain. Now try again to draw a valid conclusion.

4. Consider the following chain argument: "All libraries are quiet. Only quiet places are restful. The places where I like to study are restful." What can you conclude from the minor premise, "My bedroom is a place where I like to study"? You answered:

My bedroom is restful, quiet, and a library.

When restated, the three premises in the chain are as follows:

1. All libraries are quiet places. 2. All restful places are quiet places. 3. My study places are restful places.

--or--

1. All A are B. 2. All C are B 3. All D are C

The first two premises do not form a valid chain, since affirming A or C produces a conclusion, B, which cannot be used as the minor premise in a valid argument with the other claim. Therefore, only premises 2 and 3 form the chain. Now try again to draw a valid conclusion.

4. Consider the following chain argument: "All libraries are quiet. Only quiet places are restful. The places where I like to study are restful." What can you conclude from the minor premise, "My bedroom is a place where I like to study"? You answered:

Libraries restful and my bedroom is quiet.

When restated, the three premises in the chain are as follows:

1. All libraries are quiet places. 2. All restful places are quiet places. 3. My study places are restful places.

--or--

1. All A are B. 2. All C are B 3. All D are C

The first two premises do not form a valid chain, since affirming A or C produces a conclusion, B, which cannot be used as the minor premise in a valid argument with the other claim. Therefore, only premises 2 and 3 form the chain. Now try again to draw a valid conclusion.

Congratulations!

You have completed the exercises on universal syllogisms arguments. You may now continue with related sections on Conditionals or Non-Universal Syllogisms, or return to the Main Menu.