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 contingent truth?

  1. 2 + 2 = 4

  2. The Earth is round.

  3. The sun is a star.

  4. Humans are mortal.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The statement 'The Earth is round' is a contingent truth because it is not true in all possible worlds. For example, it is possible to imagine a world in which the Earth is flat.

Multiple choice

Which of the following is a contingent truth?

  1. I think, therefore I am.

  2. The world is real.

  3. Other minds exist.

  4. The external world exists.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The statement 'The world is real' is a contingent truth because it is not true in all possible worlds. For example, it is possible to imagine a world in which the world is not real, such as a dream world.

Multiple choice

What is the purpose of the Example (Udaharana) in the Five-Membered Syllogism?

  1. To provide a specific instance of the Reason.

  2. To introduce a new argument unrelated to the Proposition.

  3. To restate the Proposition in a different form.

  4. To provide a counterargument to the Reason.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Example (Udaharana) is the third member of the Five-Membered Syllogism. It provides a specific instance or example that illustrates the Reason and supports the Proposition. The Example helps to clarify and strengthen the argument.

Multiple choice

What is the function of the Application (Upanaya) in the Five-Membered Syllogism?

  1. To apply the Reason to the Proposition.

  2. To provide a new premise unrelated to the argument.

  3. To restate the Example in a different way.

  4. To introduce a counterargument to the Example.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Application (Upanaya) is the fourth member of the Five-Membered Syllogism. It applies the Reason to the Proposition, demonstrating how the Reason supports the Proposition. The Application shows the logical connection between the Reason and the Proposition.

Multiple choice

What is the significance of the Proposition (Pratijna) in the Five-Membered Syllogism?

  1. It establishes the main claim or conclusion to be proven.

  2. It provides evidence supporting the Reason.

  3. It illustrates the Reason with an example.

  4. It applies the Reason to the Proposition.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Proposition (Pratijna) holds significant importance in the Five-Membered Syllogism. It establishes the main claim or conclusion that the syllogism aims to prove or disprove. The Proposition serves as the foundation for the entire argument.

Multiple choice

How does the Example (Udaharana) contribute to the Five-Membered Syllogism?

  1. It provides a specific instance that supports the Reason.

  2. It introduces a new argument unrelated to the Proposition.

  3. It restates the Proposition in a different form.

  4. It provides a counterargument to the Reason.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Example (Udaharana) plays a crucial role in the Five-Membered Syllogism. It provides a specific instance or example that supports and illustrates the Reason. The Example helps to clarify and strengthen the argument by demonstrating how the Reason applies in a particular case.

Multiple choice

What is the purpose of the Application (Upanaya) in the Five-Membered Syllogism?

  1. To demonstrate the logical connection between the Reason and the Proposition.

  2. To provide a new premise unrelated to the argument.

  3. To restate the Example in a different way.

  4. To introduce a counterargument to the Example.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Application (Upanaya) serves a specific purpose in the Five-Membered Syllogism. It demonstrates the logical connection between the Reason and the Proposition. The Application shows how the Reason supports and establishes the Proposition, ensuring the validity of the argument.

Multiple choice

How does the Conclusion (Nigamana) relate to the other members of the Five-Membered Syllogism?

  1. It is the logical consequence derived from the premises.

  2. It provides evidence supporting the Reason.

  3. It illustrates the Reason with an example.

  4. It applies the Reason to the Proposition.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Conclusion (Nigamana) holds a significant position in the Five-Membered Syllogism. It is the logical consequence derived from the premises, including the Proposition, Reason, Example, and Application. The Conclusion is the final outcome of the argument and represents the established claim or proven statement.

Multiple choice

Which of the following is NOT a component of the Five-Membered Syllogism?

  1. Proposition (Pratijna)

  2. Reason (Hetu)

  3. Example (Udaharana)

  4. Counterargument (Pratijna-virodha)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Five-Membered Syllogism consists of five specific components: Proposition, Reason, Example, Application, and Conclusion. Counterargument (Pratijna-virodha) is not a component of the Five-Membered Syllogism.

Multiple choice

What is the truth value of the proposition (p ∨ q) ∧ ¬r when p is true, q is false, and r is true?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the truth table for logical operators, we have:

p q r (p ∨ q) ¬r (p ∨ q) ∧ ¬r
T F T T F F

Therefore, the truth value of the proposition is False.

Multiple choice

Which of the following is the negation of the proposition ∀x(Px → Qx)?

  1. ∃x(Px ∧ ¬Qx)

  2. ∃x(¬Px ∨ Qx)

  3. ∀x(¬Px → ¬Qx)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The negation of a universal proposition is an existential proposition with the negated predicate. Therefore, the negation of ∀x(Px → Qx) is ∃x(Px ∧ ¬Qx).

Multiple choice

Which of the following is a tautology?

  1. (p ∨ q) → (¬p → q)

  2. (p ∧ q) → (p → q)

  3. (p → q) → (¬q → ¬p)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A tautology is a proposition that is true for all possible combinations of truth values of its variables. Using the truth table for logical operators, we can verify that the proposition (p ∨ q) → (¬p → q) is true for all possible combinations of truth values of p and q. Therefore, it is a tautology.

Multiple choice

What is the dual of the following propositional formula: (p ∨ q) ∧ (¬p ∨ r)?

  1. ¬(p ∧ q) ∨ ¬(¬p ∧ r)

  2. (¬p ∧ q) ∨ (p ∧ r)

  3. (p ∧ ¬q) ∨ (¬p ∧ r)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The dual of a propositional formula is obtained by replacing each variable with its negation and each logical operator with its dual. The dual of ∨ is ∧, and the dual of ∧ is ∨. Therefore, the dual of (p ∨ q) ∧ (¬p ∨ r) is (¬p ∧ q) ∨ (p ∧ r).

Multiple choice

What is the De Morgan's law for negation of a conjunction?

  1. ¬(p ∧ q) = ¬p ∨ ¬q

  2. ¬(p ∨ q) = ¬p ∧ ¬q

  3. ¬(p → q) = ¬p ∨ q

  4. ¬(p ⊕ q) = ¬p ∧ q
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

De Morgan's law for negation of a conjunction states that the negation of a conjunction of two propositions is equivalent to the disjunction of their negations. In other words, ¬(p ∧ q) = ¬p ∨ ¬q.

Multiple choice

What is the distributive law for conjunction over disjunction?

  1. p ∧ (q ∨ r) = (p ∧ q) ∨ (p ∧ r)

  2. p ∨ (q ∧ r) = (p ∨ q) ∧ (p ∨ r)

  3. p → (q ∨ r) = (p → q) ∨ (p → r)

  4. p ⊕ (q ∧ r) = (p ⊕ q) ∧ (p ⊕ r)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The distributive law for conjunction over disjunction states that the conjunction of a proposition with the disjunction of two other propositions is equivalent to the disjunction of the conjunction of the first proposition with each of the other two propositions. In other words, p ∧ (q ∨ r) = (p ∧ q) ∨ (p ∧ r).