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Mathematical Methods and Reasoning

Description: Mathematical Methods and Reasoning Quiz
Number of Questions: 14
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Tags: mathematical methods reasoning philosophy of mathematics
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Which of the following is not a mathematical method?

  1. Induction

  2. Deduction

  3. Analogy

  4. Experimentation

Show answer
Correct Option: D
Explanation:

Experimentation is a scientific method, not a mathematical method.

What is the process of reasoning from a general statement to a specific conclusion called?

  1. Induction

  2. Deduction

  3. Analogy

  4. Syllogism

Show answer
Correct Option: B
Explanation:

Deduction is the process of reasoning from a general statement to a specific conclusion.

What is the process of reasoning from a specific example to a general conclusion called?

  1. Induction

  2. Deduction

  3. Analogy

  4. Syllogism

Show answer
Correct Option: A
Explanation:

Induction is the process of reasoning from a specific example to a general conclusion.

What is the process of reasoning from one specific example to another specific example called?

  1. Induction

  2. Deduction

  3. Analogy

  4. Syllogism

Show answer
Correct Option: C
Explanation:

Analogy is the process of reasoning from one specific example to another specific example.

What is a logical argument that consists of two premises and a conclusion called?

  1. Induction

  2. Deduction

  3. Analogy

  4. Syllogism

Show answer
Correct Option: D
Explanation:

A syllogism is a logical argument that consists of two premises and a conclusion.

Which of the following is an example of a valid syllogism?

  1. All men are mortal. Socrates is a man. Therefore, Socrates is mortal.

  2. All dogs are mammals. All mammals are animals. Therefore, all dogs are animals.

  3. Some birds can fly. All eagles are birds. Therefore, all eagles can fly.

  4. No cats are dogs. All dogs are animals. Therefore, no cats are animals.

Show answer
Correct Option: A
Explanation:

A valid syllogism is one in which the conclusion follows logically from the premises.

Which of the following is an example of an invalid syllogism?

  1. All men are mortal. Socrates is a man. Therefore, Socrates is mortal.

  2. All dogs are mammals. All mammals are animals. Therefore, all dogs are animals.

  3. Some birds can fly. All eagles are birds. Therefore, all eagles can fly.

  4. No cats are dogs. All dogs are animals. Therefore, no cats are animals.

Show answer
Correct Option: D
Explanation:

An invalid syllogism is one in which the conclusion does not follow logically from the premises.

What is the difference between a deductive argument and an inductive argument?

  1. A deductive argument is based on evidence, while an inductive argument is based on logic.

  2. A deductive argument is based on logic, while an inductive argument is based on evidence.

  3. A deductive argument is based on a priori knowledge, while an inductive argument is based on a posteriori knowledge.

  4. A deductive argument is based on a posteriori knowledge, while an inductive argument is based on a priori knowledge.

Show answer
Correct Option: B
Explanation:

A deductive argument is based on logic, while an inductive argument is based on evidence.

What is the difference between a priori knowledge and a posteriori knowledge?

  1. A priori knowledge is knowledge that is gained through experience, while a posteriori knowledge is knowledge that is gained through reason.

  2. A priori knowledge is knowledge that is gained through reason, while a posteriori knowledge is knowledge that is gained through experience.

  3. A priori knowledge is knowledge that is true by definition, while a posteriori knowledge is knowledge that is true by experience.

  4. A posteriori knowledge is knowledge that is true by definition, while a priori knowledge is knowledge that is true by experience.

Show answer
Correct Option: B
Explanation:

A priori knowledge is knowledge that is gained through reason, while a posteriori knowledge is knowledge that is gained through experience.

What is the difference between a necessary truth and a contingent truth?

  1. A necessary truth is a truth that is true in all possible worlds, while a contingent truth is a truth that is true in some possible worlds but not in others.

  2. A necessary truth is a truth that is true in some possible worlds but not in others, while a contingent truth is a truth that is true in all possible worlds.

  3. A necessary truth is a truth that is true by definition, while a contingent truth is a truth that is true by experience.

  4. A contingent truth is a truth that is true by definition, while a necessary truth is a truth that is true by experience.

Show answer
Correct Option: A
Explanation:

A necessary truth is a truth that is true in all possible worlds, while a contingent truth is a truth that is true in some possible worlds but not in others.

What is the difference between a categorical statement and a hypothetical statement?

  1. A categorical statement is a statement that is either true or false, while a hypothetical statement is a statement that is either true or false depending on the truth of its antecedent.

  2. A categorical statement is a statement that is either true or false depending on the truth of its antecedent, while a hypothetical statement is a statement that is either true or false.

  3. A categorical statement is a statement that is true in all possible worlds, while a hypothetical statement is a statement that is true in some possible worlds but not in others.

  4. A hypothetical statement is a statement that is true in all possible worlds, while a categorical statement is a statement that is true in some possible worlds but not in others.

Show answer
Correct Option: A
Explanation:

A categorical statement is a statement that is either true or false, while a hypothetical statement is a statement that is either true or false depending on the truth of its antecedent.

What is the difference between a deductive argument and an inductive argument?

  1. A deductive argument is a valid argument in which the conclusion follows logically from the premises, while an inductive argument is an invalid argument in which the conclusion does not follow logically from the premises.

  2. A deductive argument is an invalid argument in which the conclusion does not follow logically from the premises, while an inductive argument is a valid argument in which the conclusion follows logically from the premises.

  3. A deductive argument is a valid argument in which the conclusion is true if the premises are true, while an inductive argument is an invalid argument in which the conclusion is not necessarily true even if the premises are true.

  4. A deductive argument is an invalid argument in which the conclusion is not necessarily true even if the premises are true, while an inductive argument is a valid argument in which the conclusion is true if the premises are true.

Show answer
Correct Option: A
Explanation:

A deductive argument is a valid argument in which the conclusion follows logically from the premises, while an inductive argument is an invalid argument in which the conclusion does not follow logically from the premises.

What is the difference between a necessary truth and a contingent truth?

  1. A necessary truth is a truth that is true in all possible worlds, while a contingent truth is a truth that is true in some possible worlds but not in others.

  2. A necessary truth is a truth that is true in some possible worlds but not in others, while a contingent truth is a truth that is true in all possible worlds.

  3. A necessary truth is a truth that is true by definition, while a contingent truth is a truth that is true by experience.

  4. A contingent truth is a truth that is true by definition, while a necessary truth is a truth that is true by experience.

Show answer
Correct Option: A
Explanation:

A necessary truth is a truth that is true in all possible worlds, while a contingent truth is a truth that is true in some possible worlds but not in others.

What is the difference between a categorical statement and a hypothetical statement?

  1. A categorical statement is a statement that is either true or false, while a hypothetical statement is a statement that is either true or false depending on the truth of its antecedent.

  2. A categorical statement is a statement that is either true or false depending on the truth of its antecedent, while a hypothetical statement is a statement that is either true or false.

  3. A categorical statement is a statement that is true in all possible worlds, while a hypothetical statement is a statement that is true in some possible worlds but not in others.

  4. A hypothetical statement is a statement that is true in all possible worlds, while a categorical statement is a statement that is true in some possible worlds but not in others.

Show answer
Correct Option: A
Explanation:

A categorical statement is a statement that is either true or false, while a hypothetical statement is a statement that is either true or false depending on the truth of its antecedent.

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