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Propositional Logic: Logical Arguments and Formal Fallacies

Description: Propositional Logic: Logical Arguments and Formal Fallacies
Number of Questions: 15
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Tags: propositional logic logical arguments formal fallacies
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Which of the following is a valid logical argument?

  1. If it is raining, then the ground is wet. It is raining. Therefore, the ground is wet.

  2. If it is raining, then the ground is wet. The ground is not wet. Therefore, it is not raining.

  3. If it is raining, then the ground is wet. It is not raining. Therefore, the ground is not wet.


Correct Option: A
Explanation:

This is a valid argument because the conclusion follows logically from the premises. If it is raining, then the ground is wet. It is raining. Therefore, the ground is wet.

Which of the following is a formal fallacy?

  1. Affirming the consequent

  2. Denying the antecedent

  3. Appeal to emotion


Correct Option: A
Explanation:

Affirming the consequent is a formal fallacy that occurs when someone assumes that because the consequent of a conditional statement is true, the antecedent must also be true. For example, "If it is raining, then the ground is wet. The ground is wet. Therefore, it is raining." This is a fallacy because the ground could be wet for other reasons, such as someone watering the lawn.

What is the difference between a logical argument and a formal fallacy?

  1. A logical argument is always valid, while a formal fallacy is always invalid.

  2. A logical argument is based on evidence, while a formal fallacy is based on emotion.

  3. A logical argument is always true, while a formal fallacy is always false.


Correct Option: A
Explanation:

A logical argument is a series of statements in which the conclusion follows logically from the premises. A formal fallacy is a type of argument that is always invalid, regardless of the truth of the premises. This means that the conclusion of a formal fallacy does not follow logically from the premises.

Which of the following is an example of a deductive argument?

  1. All dogs are mammals. Fido is a dog. Therefore, Fido is a mammal.

  2. Most people like chocolate. I am a person. Therefore, I like chocolate.

  3. The sky is blue. The grass is green. Therefore, the sky is not green.


Correct Option: A
Explanation:

A deductive argument is a type of argument in which the conclusion is guaranteed to be true if the premises are true. In the example above, the premises are "All dogs are mammals" and "Fido is a dog." The conclusion is "Therefore, Fido is a mammal." Since the premises are true, the conclusion must also be true.

Which of the following is an example of an inductive argument?

  1. All dogs are mammals. Fido is a dog. Therefore, Fido is a mammal.

  2. Most people like chocolate. I am a person. Therefore, I like chocolate.

  3. The sky is blue. The grass is green. Therefore, the sky is not green.


Correct Option: B
Explanation:

An inductive argument is a type of argument in which the conclusion is not guaranteed to be true, even if the premises are true. In the example above, the premises are "Most people like chocolate" and "I am a person." The conclusion is "Therefore, I like chocolate." Since the premises are not certain, the conclusion is also not certain.

Which of the following is an example of a syllogism?

  1. All dogs are mammals. Fido is a dog. Therefore, Fido is a mammal.

  2. Most people like chocolate. I am a person. Therefore, I like chocolate.

  3. The sky is blue. The grass is green. Therefore, the sky is not green.


Correct Option: A
Explanation:

A syllogism is a type of deductive argument that consists of three parts: a major premise, a minor premise, and a conclusion. The major premise is a general statement about a category of things. The minor premise is a statement about a specific member of that category. The conclusion is a statement about the specific member of the category that follows logically from the major and minor premises. In the example above, the major premise is "All dogs are mammals." The minor premise is "Fido is a dog." The conclusion is "Therefore, Fido is a mammal."

Which of the following is an example of a categorical proposition?

  1. All dogs are mammals.

  2. Some dogs are black.

  3. No dogs are cats.


Correct Option: A
Explanation:

A categorical proposition is a type of proposition that makes a general statement about a category of things. In the example above, the proposition "All dogs are mammals" is a categorical proposition because it makes a general statement about the category of dogs.

Which of the following is an example of a hypothetical proposition?

  1. If it is raining, then the ground is wet.

  2. Either it is raining or it is not raining.

  3. It is raining and the ground is wet.


Correct Option: A
Explanation:

A hypothetical proposition is a type of proposition that makes a statement about the relationship between two or more propositions. In the example above, the proposition "If it is raining, then the ground is wet." is a hypothetical proposition because it makes a statement about the relationship between the proposition "It is raining" and the proposition "The ground is wet."

Which of the following is an example of a disjunctive proposition?

  1. Either it is raining or it is not raining.

  2. It is raining and the ground is wet.

  3. All dogs are mammals.


Correct Option: A
Explanation:

A disjunctive proposition is a type of proposition that makes a statement about the relationship between two or more propositions. In the example above, the proposition "Either it is raining or it is not raining." is a disjunctive proposition because it makes a statement about the relationship between the proposition "It is raining" and the proposition "It is not raining."

Which of the following is an example of a conjunctive proposition?

  1. It is raining and the ground is wet.

  2. Either it is raining or it is not raining.

  3. All dogs are mammals.


Correct Option: A
Explanation:

A conjunctive proposition is a type of proposition that makes a statement about the relationship between two or more propositions. In the example above, the proposition "It is raining and the ground is wet." is a conjunctive proposition because it makes a statement about the relationship between the proposition "It is raining" and the proposition "The ground is wet."

Which of the following is an example of a negation proposition?

  1. It is not raining.

  2. Either it is raining or it is not raining.

  3. All dogs are mammals.


Correct Option: A
Explanation:

A negation proposition is a type of proposition that makes a statement about the truth or falsity of another proposition. In the example above, the proposition "It is not raining." is a negation proposition because it makes a statement about the truth or falsity of the proposition "It is raining."

Which of the following is an example of a tautology?

  1. If it is raining, then it is raining.

  2. Either it is raining or it is not raining.

  3. All dogs are mammals.


Correct Option: A
Explanation:

A tautology is a type of proposition that is always true, regardless of the truth or falsity of its component propositions. In the example above, the proposition "If it is raining, then it is raining." is a tautology because it is always true, regardless of whether it is actually raining or not.

Which of the following is an example of a contradiction?

  1. It is raining and it is not raining.

  2. Either it is raining or it is not raining.

  3. All dogs are mammals.


Correct Option: A
Explanation:

A contradiction is a type of proposition that is always false, regardless of the truth or falsity of its component propositions. In the example above, the proposition "It is raining and it is not raining." is a contradiction because it is always false, regardless of whether it is actually raining or not.

Which of the following is an example of a contingency?

  1. It is raining.

  2. Either it is raining or it is not raining.

  3. All dogs are mammals.


Correct Option: A
Explanation:

A contingency is a type of proposition that is neither a tautology nor a contradiction. In other words, it is a proposition that is sometimes true and sometimes false. In the example above, the proposition "It is raining." is a contingency because it is sometimes true and sometimes false, depending on the weather.

Which of the following is an example of a modal proposition?

  1. It is possible that it is raining.

  2. Either it is raining or it is not raining.

  3. All dogs are mammals.


Correct Option: A
Explanation:

A modal proposition is a type of proposition that makes a statement about the possibility, necessity, or impossibility of another proposition. In the example above, the proposition "It is possible that it is raining." is a modal proposition because it makes a statement about the possibility of the proposition "It is raining."

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