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

Which of the following is a valid inference rule in propositional logic?

  1. Modus Ponens

  2. Modus Tollens

  3. Hypothetical Syllogism

  4. Disjunctive Syllogism
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Modus Ponens is a valid inference rule that allows us to infer P from the premises P → Q and Q.

Multiple choice

Which of the following is an example of a valid argument in first-order logic?

  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. Tweety is a bird. Therefore, Tweety can fly.

  4. No cats are dogs. Garfield is a cat. Therefore, Garfield is not a dog.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A valid argument is an argument in which the conclusion follows logically from the premises.

Multiple choice

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

  1. The sky is blue. Therefore, the grass is green.

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

  3. I saw a black cat yesterday. Therefore, all cats are black.

  4. I like chocolate ice cream. Therefore, everyone likes chocolate ice cream.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A deductive argument is an argument in which the conclusion is guaranteed to be true if the premises are true.

Multiple choice

Which of the following is an example of a non-constructive proof?

  1. Proof by contradiction

  2. Proof by mathematical induction

  3. Proof by exhaustion

  4. Proof by construction
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A non-constructive proof is a proof that shows that a statement is true without actually providing a way to construct the object that the statement claims exists.

Multiple choice

What is the dual of the expression (A ∨ B) ∧ (C ∧ D)?

  1. ¬(¬A ∧ ¬B) ∨ ¬(¬C ∨ ¬D)

  2. ¬(¬A ∨ ¬B) ∧ ¬(¬C ∧ ¬D)

  3. ¬(A ∧ B) ∨ ¬(C ∨ D)

  4. ¬(A ∨ B) ∧ ¬(C ∧ D)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The dual of a Boolean expression is obtained by interchanging ∨ and ∧, and 0 and 1.

Multiple choice

Which of the following is a valid Boolean identity?

  1. ¬(A ∨ B) = ¬A ∨ ¬B

  2. ¬(A ∧ B) = ¬A ∧ ¬B

  3. A ∨ B = A ∧ B

  4. A ∧ B = A ∨ B
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

De Morgan's law states that the negation of a disjunction is the conjunction of the negations, and vice versa. Therefore, ¬(A ∨ B) = ¬A ∨ ¬B is a valid Boolean identity.

Multiple choice

What is the complement of the Boolean expression (A ∧ B) ∨ (¬A ∧ C)?

  1. ¬(A ∧ B) ∧ ¬(¬A ∧ C)

  2. ¬(A ∧ B) ∨ ¬(¬A ∧ C)

  3. (A ∨ B) ∧ (¬A ∨ C)

  4. (A ∨ B) ∨ (¬A ∨ C)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The complement of a Boolean expression is obtained by negating the entire expression. Therefore, the complement of (A ∧ B) ∨ (¬A ∧ C) is ¬(A ∧ B) ∧ ¬(¬A ∧ C).

Multiple choice

What is the dual of the Boolean expression (A ∧ B) ∨ (¬A ∧ C)?

  1. ¬(¬A ∨ ¬B) ∧ ¬(A ∨ ¬C)

  2. ¬(¬A ∨ ¬B) ∨ ¬(A ∨ ¬C)

  3. ¬(A ∨ B) ∧ ¬(¬A ∨ C)

  4. ¬(A ∨ B) ∨ ¬(¬A ∨ C)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The dual of a Boolean expression is obtained by interchanging ∨ and ∧, and 0 and 1. Therefore, the dual of (A ∧ B) ∨ (¬A ∧ C) is ¬(¬A ∨ ¬B) ∧ ¬(A ∨ ¬C).

Multiple choice

Which of the following is a valid Boolean identity?

  1. ¬(A ∨ B) = ¬A ∨ ¬B

  2. ¬(A ∧ B) = ¬A ∧ ¬B

  3. A ∨ B = A ∧ B

  4. A ∧ B = A ∨ B
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

De Morgan's law states that the negation of a disjunction is the conjunction of the negations, and vice versa. Therefore, ¬(A ∨ B) = ¬A ∨ ¬B is a valid Boolean identity.

Multiple choice

What is the complement of the Boolean expression (A ∧ B) ∨ (¬A ∧ C)?

  1. ¬(A ∧ B) ∧ ¬(¬A ∧ C)

  2. ¬(A ∧ B) ∨ ¬(¬A ∧ C)

  3. (A ∨ B) ∧ (¬A ∨ C)

  4. (A ∨ B) ∨ (¬A ∨ C)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The complement of a Boolean expression is obtained by negating the entire expression. Therefore, the complement of (A ∧ B) ∨ (¬A ∧ C) is ¬(A ∧ B) ∧ ¬(¬A ∧ C).

Multiple choice

Which of the following is NOT a type of inference recognized by the Nyaya-Vaiseshika school?

  1. Deductive inference

  2. Inductive inference

  3. Analogical inference

  4. Hypothetical inference

  5. Disjunctive inference
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Hypothetical inference is not recognized as a valid type of inference in the Nyaya-Vaiseshika system.

Multiple choice

What is the term used in Nyaya-Vaiseshika philosophy to refer to the process of reasoning from a general principle to a specific instance?

  1. Deductive inference

  2. Inductive inference

  3. Analogical inference

  4. Hypothetical inference

  5. Disjunctive inference
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Deductive inference, or 'anumana,' is the process of reasoning from a general principle to a specific instance.

Multiple choice

What is the term used in Nyaya-Vaiseshika philosophy to refer to the process of reasoning from a specific instance to a general principle?

  1. Deductive inference

  2. Inductive inference

  3. Analogical inference

  4. Hypothetical inference

  5. Disjunctive inference
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Inductive inference, or 'vyapti,' is the process of reasoning from a specific instance to a general principle.

Multiple choice

In the context of mathematics and metaphysics, what does the term 'axioms' refer to?

  1. Self-evident truths that serve as the foundation for mathematical reasoning

  2. Arbitrary statements that are assumed to be true for the sake of mathematical exploration

  3. Mathematical propositions that can be derived from other axioms or theorems

  4. Complex mathematical equations that describe physical phenomena
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Axioms are fundamental statements in mathematics that are considered to be self-evidently true and serve as the basis for deductive reasoning.

Multiple choice

Which mathematical principle asserts that every mathematical statement can be either proven or disproven?

  1. The Law of Excluded Middle

  2. The Law of Non-Contradiction

  3. The Axiom of Choice

  4. The Completeness Theorem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Law of Excluded Middle states that for any proposition, either it or its negation is true, allowing for a binary division of truth values.