Reasoning

Logic and Fallacies

1,803 Questions

Understand the fundamentals of propositional logic, logical inference rules, and paradoxes. This set includes identifying logical fallacies, including those found in classical Nyaya logic. Strong grasp of these concepts is crucial for scoring well in the reasoning sections of competitive tests.

Propositional logic modelsLogical inference rulesTypes of logical fallaciesParadoxes and contingent truthsNyaya logic concepts

Logic and Fallacies Questions

Multiple choice

What is the difference between a proof by exhaustion and a proof by contradiction?

  1. A proof by exhaustion proves a statement by considering all possible cases.

  2. A proof by contradiction proves a statement by showing that its negation is false.

  3. A proof by exhaustion uses logic to reach a conclusion, while a proof by contradiction uses evidence to reach a conclusion.

  4. A proof by exhaustion is always valid, while a proof by contradiction is sometimes valid.
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Explanation

A proof by exhaustion proves a statement by considering all possible cases. A proof by contradiction proves a statement by showing that its negation is false. For example, the statement "There are only a finite number of prime numbers" can be proven by exhaustion by showing that there are only a finite number of prime numbers less than any given number. It can also be proven by contradiction by showing that the negation of the statement, "There are an infinite number of prime numbers", is false.

Multiple choice

What is the difference between a proof by cases and a proof by contradiction?

  1. A proof by cases proves a statement by considering all possible cases.

  2. A proof by contradiction proves a statement by showing that its negation is false.

  3. A proof by cases uses logic to reach a conclusion, while a proof by contradiction uses evidence to reach a conclusion.

  4. A proof by cases is always valid, while a proof by contradiction is sometimes valid.
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Explanation

A proof by cases proves a statement by considering all possible cases. A proof by contradiction proves a statement by showing that its negation is false. For example, the statement "Every integer is either even or odd" can be proven by cases by considering all possible cases: an integer is either even or odd. It can also be proven by contradiction by showing that the negation of the statement, "There exists an integer that is neither even nor odd", is false.

Multiple choice

What is the name of the famous theorem that proved the existence of undecidable statements in any formal system capable of expressing basic arithmetic?

  1. Gödel's Incompleteness Theorem

  2. Russell's Paradox

  3. The Liar's Paradox

  4. Zeno's Paradox
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Explanation

Gödel's Incompleteness Theorem, formulated by Kurt Gödel in 1931, demonstrated that any formal system capable of expressing basic arithmetic must either be incomplete or inconsistent.

Multiple choice

What is the most common response to the argument from logic?

  1. The argument from intuition.

  2. The argument from science.

  3. The argument from morality.

  4. The argument from other minds.
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Explanation

The most common response to the argument from logic is the argument from intuition. This argument states that even if it is logically impossible for free will to be compatible with determinism, we still have an intuitive sense that we have free will. This intuitive sense of free will is difficult to deny, even if we accept the argument from logic.

Multiple choice

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

  1. All men are mortal.

  2. Socrates is a man.

  3. Therefore, Socrates is mortal.

  4. All swans are white.

  5. I have seen many white swans.

  6. Therefore, all swans are white.
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Correct answer
Explanation

This is an inductive argument because it uses evidence (the fact that I have seen many white swans) to support a conclusion (that all swans are white). However, the conclusion is not necessarily true, because it is possible that there are black swans that I have not seen.

Multiple choice

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

  1. All men are mortal.

  2. Socrates is a man.

  3. Therefore, Socrates is mortal.

  4. All swans are white.

  5. I have seen many white swans.

  6. Therefore, all swans are white.
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Explanation

This is a deductive argument because the conclusion (that Socrates is mortal) is guaranteed to be true if the premises (that all men are mortal and that Socrates is a man) are true.

Multiple choice

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

  1. All swans are white.

  2. I have seen many white swans.

  3. Therefore, all swans are white.

  4. Most people who smoke cigarettes get lung cancer.

  5. I know someone who smoked cigarettes and got lung cancer.

  6. Therefore, most people who smoke cigarettes get lung cancer.
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Correct answer
Explanation

This is a strong inductive argument because the evidence (the fact that I know someone who smoked cigarettes and got lung cancer) is relevant to the conclusion (that most people who smoke cigarettes get lung cancer). The evidence is also strong because it is based on a large sample size (the population of people who smoke cigarettes).

Multiple choice

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

  1. All swans are white.

  2. I have seen many white swans.

  3. Therefore, all swans are white.

  4. Most people who smoke cigarettes get lung cancer.

  5. I know someone who smoked cigarettes and got lung cancer.

  6. Therefore, most people who smoke cigarettes get lung cancer.
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Correct answer
Explanation

This is a weak inductive argument because the evidence (the fact that I have seen many white swans) is not relevant to the conclusion (that all swans are white). The evidence is also weak because it is based on a small sample size (the number of white swans that I have seen).

Multiple choice

What is the fallacy of affirming the consequent?

  1. Assuming that the conclusion of an argument is true and then using that assumption to prove the premises of the argument.

  2. Assuming that the premises of an argument are true and then using that assumption to prove the conclusion of the argument.

  3. Assuming that one premise of an argument is true and then using that assumption to prove the other premise of the argument.

  4. Assuming that the conclusion of an argument is false and then using that assumption to prove the premises of the argument.
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Explanation

The fallacy of affirming the consequent is assuming that the conclusion of an argument is true and then using that assumption to prove the premises of the argument. This is a fallacy because it is possible for the conclusion of an argument to be true even if the premises are false.

Multiple choice

What is the fallacy of denying the antecedent?

  1. Assuming that the conclusion of an argument is true and then using that assumption to prove the premises of the argument.

  2. Assuming that the premises of an argument are true and then using that assumption to prove the conclusion of the argument.

  3. Assuming that one premise of an argument is true and then using that assumption to prove the other premise of the argument.

  4. Assuming that the conclusion of an argument is false and then using that assumption to prove the premises of the argument.
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Explanation

The fallacy of denying the antecedent is assuming that the conclusion of an argument is false and then using that assumption to prove the premises of the argument. This is a fallacy because it is possible for the conclusion of an argument to be false even if the premises are true.

Multiple choice

Which of the following is an example of a fallacy?

  1. All men are mortal.

  2. Socrates is a man.

  3. Therefore, Socrates is mortal.

  4. All swans are white.

  5. I have seen many white swans.

  6. Therefore, all swans are white.
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Correct answer
Explanation

This is an example of a fallacy because the reasoning is invalid. The fact that I have seen many white swans does not necessarily mean that all swans are white. It is possible that there are black swans that I have not seen.

Multiple choice

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

  1. All men are mortal.

  2. Socrates is a man.

  3. Therefore, Socrates is mortal.

  4. All swans are white.

  5. I have seen many white swans.

  6. Therefore, all swans are white.
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Correct answer
Explanation

This is an example of a valid argument because the reasoning is valid. The conclusion (that Socrates is mortal) follows logically from the premises (that all men are mortal and that Socrates is a man).

Multiple choice

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

  1. All men are mortal.

  2. Socrates is a man.

  3. Therefore, Socrates is mortal.

  4. All swans are white.

  5. I have seen many white swans.

  6. Therefore, all swans are white.
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Correct answer
Explanation

This is an example of a sound argument because it is both valid and true. The premises (that all men are mortal and that Socrates is a man) are true, and the conclusion (that Socrates is mortal) follows logically from the premises.

Multiple choice

Which of the following is an example of a valid but unsound argument?

  1. All men are mortal.

  2. Socrates is a man.

  3. Therefore, Socrates is mortal.

  4. All swans are white.

  5. I have seen many white swans.

  6. Therefore, all swans are white.
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Correct answer
Explanation

This is an example of a valid but unsound argument because it is valid but not true. The premises (that I have seen many white swans) are true, but the conclusion (that all swans are white) is not necessarily true. It is possible that there are black swans that I have not seen.

Multiple choice

What is the most famous example of the Liar Paradox?

  1. The statement 'This statement is false.'

  2. The statement 'I am lying.'

  3. The statement 'All statements are false.'

  4. The statement 'Truth is relative.'
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Explanation

The most famous example of the Liar Paradox is the statement 'This statement is false.' If this statement is true, then it must be false, and vice versa. This leads to a contradiction, which shows that the statement cannot be either true or false.