Reasoning

Logic and Fallacies

1,716 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

Which of the following is an example of a pragmatic truth?

  1. The sky is blue.

  2. The sun is a star.

  3. The Earth is flat.

  4. All of the above
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A Correct answer
Explanation

The statement "The sky is blue" is a pragmatic truth. It is true in most cases, but it is not true in all cases. For example, the sky can be gray or black on a cloudy day.

Multiple choice

Which of the following is an example of a semantic truth?

  1. The sky is blue.

  2. The sun is a star.

  3. The Earth is flat.

  4. All of the above
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Correct answer
Explanation

None of the statements listed are semantic truths. The sky is not always blue, the sun is not always a star, and the Earth is not flat.

Multiple choice

Which of the following is an example of a pragmatic truth?

  1. The sky is blue.

  2. The sun is a star.

  3. The Earth is flat.

  4. All of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The statement "The sky is blue" is a pragmatic truth. It is true in most cases, but it is not true in all cases. For example, the sky can be gray or black on a cloudy day.

Multiple choice

What is the No True Scotsman fallacy?

  1. A logical fallacy that occurs when someone changes the definition of a term in order to exclude an unwanted example.

  2. A logical fallacy that occurs when someone assumes that something is true because it is widely believed.

  3. A logical fallacy that occurs when someone appeals to emotion in order to support their argument.

  4. A logical fallacy that occurs when someone uses a circular argument.
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A Correct answer
Explanation

The No True Scotsman fallacy is a logical fallacy that occurs when someone changes the definition of a term in order to exclude an unwanted example. This fallacy is often used in response to the Gettier Problem, where someone might argue that a Gettier case is not a genuine case of knowledge because it does not meet the new definition of knowledge.

Multiple choice

Is it possible to have a justified belief that is not true?

  1. Yes

  2. No
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A Correct answer
Explanation

It is possible to have a justified belief that is not true. For example, you might believe that your friend is going to pass their exam because they studied hard. This belief is justified because you have evidence to support it (your friend's hard work), but it is not true if your friend does not pass their exam.

Multiple choice

Which of the following is a consequence of the Choice Axiom?

  1. The Well-Ordering Principle

  2. Zorn's Lemma

  3. The Axiom of Infinity

  4. The Continuum Hypothesis
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A Correct answer
Explanation

The Well-Ordering Principle states that every set can be well-ordered, which means it can be arranged in a sequence such that each element is either the first element or follows a unique predecessor. This principle is a consequence of the Choice Axiom.

Multiple choice

The Choice Axiom is independent of which other axiom of set theory?

  1. The Axiom of Infinity

  2. The Axiom of Power Set

  3. The Axiom of Extensionality

  4. The Axiom of Regularity
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Choice Axiom is independent of the Axiom of Infinity. This means that it is possible to construct models of set theory in which the Choice Axiom holds but the Axiom of Infinity does not, and vice versa.

Multiple choice

Which of the following is a controversial implication of the Choice Axiom?

  1. The Banach-Tarski Paradox

  2. The Russell's Paradox

  3. The Schroeder-Bernstein Theorem

  4. The Cantor-Bernstein Theorem
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A Correct answer
Explanation

The Banach-Tarski Paradox is a controversial implication of the Choice Axiom. It states that it is possible to decompose a solid ball into a finite number of pieces and then reassemble them into two balls of the same size as the original ball.

Multiple choice

Which of the following is an example of a mathematical statement that requires the Choice Axiom for its proof?

  1. The existence of a well-ordering of the real numbers.

  2. The existence of a maximal element in every non-empty partially ordered set.

  3. The existence of a choice function for every non-empty collection of non-empty sets.

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

All of the above statements require the Choice Axiom for their proof.

Multiple choice

What is the status of the Choice Axiom in modern mathematics?

  1. It is generally accepted as a valid axiom of set theory.

  2. It is rejected by some mathematicians due to its counterintuitive consequences.

  3. Its status is still being debated among mathematicians.

  4. None of the above
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A Correct answer
Explanation

Despite its controversial nature, the Choice Axiom is generally accepted as a valid axiom of set theory and is widely used in mathematical research.

Multiple choice

What is the 'Frankfurt-style' counterexample to the principle of alternate possibilities?

  1. The case of the man who is forced to choose between saving his wife or his child.

  2. The case of the man who is hypnotized to believe that he is a chicken.

  3. The case of the man who is given a drug that makes him unable to control his actions.

  4. All of the above.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Frankfurt-style counterexamples challenge the principle of alternate possibilities, which is often used to argue for the necessity of free will.

Multiple choice

Which of the following is a valid formula in second-order predicate logic?

  1. $\exists x \forall y P(x, y)$
  2. $\forall x \exists y P(x, y)$
  3. $\exists P \forall x P(x)$
  4. $\forall P \exists x P(x)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In second-order predicate logic, it is possible to quantify over predicates. The formula $\exists P \forall x P(x)$ means that there exists a property $P$ such that for all individuals $x$, $P(x)$ is true.

Multiple choice

What is the Completeness theorem?

  1. A theorem that states that every valid formula in first-order predicate logic is provable.

  2. A theorem that states that every valid formula in second-order predicate logic is provable.

  3. A theorem that states that every satisfiable formula in first-order predicate logic is provable.

  4. A theorem that states that every satisfiable formula in second-order predicate logic is provable.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Completeness theorem is a fundamental result in mathematical logic that states that every valid formula in first-order predicate logic is provable. This means that if a formula is true in every model of first-order predicate logic, then it can be proven using the rules of first-order predicate logic.

Multiple choice

What is the Gödel's incompleteness theorem?

  1. A theorem that states that every consistent first-order theory is either incomplete or unsound.

  2. A theorem that states that every consistent second-order theory is either incomplete or unsound.

  3. A theorem that states that every consistent first-order theory is either complete or unsound.

  4. A theorem that states that every consistent second-order theory is either complete or unsound.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Gödel's incompleteness theorem is a fundamental result in mathematical logic that states that every consistent first-order theory is either incomplete or unsound. This means that there are true statements about the natural numbers that cannot be proven using the rules of first-order logic.

Multiple choice

What is the difference between a satisfiability and a validity in second-order predicate logic?

  1. A formula is satisfiable if there exists a model in which the formula is true, and a formula is valid if it is true in all models.

  2. A formula is satisfiable if there exists a model in which the formula is false, and a formula is valid if it is false in all models.

  3. A formula is satisfiable if there exists a model in which the formula is true, and a formula is valid if it is false in all models.

  4. A formula is satisfiable if there exists a model in which the formula is false, and a formula is valid if it is true in all models.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In second-order predicate logic, a formula is satisfiable if there exists a model in which the formula is true, and a formula is valid if it is true in all models.