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

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).

Multiple choice

Which of the following is an example of a tautology?

  1. p ∨ ¬p

  2. p ∧ ¬p

  3. p → q

  4. p ⊕ q
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. The proposition p ∨ ¬p is a tautology because it is true for all possible combinations of truth values of p. This can be verified using the truth table for the logical operators ∨ and ¬.

Multiple choice

Which fallacy is commonly discussed in the Nyaya School's theory of inference?

  1. Affirming the Consequent

  2. Denying the Antecedent

  3. Appeal to Ignorance

  4. Ad Hominem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Affirming the Consequent is a common fallacy discussed in the Nyaya School's theory of inference.

Multiple choice

Which of the following is not a major problem in the Philosophy of Mathematics?

  1. The problem of universals

  2. The problem of induction

  3. The problem of free will

  4. The problem of evil
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The problem of free will is not a major problem in the Philosophy of Mathematics.

Multiple choice

What is the role of entailment in relevant logic?

  1. Entailment is a necessary condition for a valid argument.

  2. Entailment is a sufficient condition for a valid argument.

  3. Entailment is both a necessary and sufficient condition for a valid argument.

  4. Entailment is not a necessary or sufficient condition for a valid argument.

  5. Entailment is a type of logical fallacy.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In relevant logic, entailment is a necessary condition for a valid argument, meaning that if the premises of an argument entail the conclusion, then the argument is valid.

Multiple choice

How does relevant logic differ from other non-classical logics?

  1. Relevant logic is based on a different set of axioms.

  2. Relevant logic uses a different type of inference rule.

  3. Relevant logic has a different interpretation of truth.

  4. Relevant logic is more complex than other non-classical logics.

  5. Relevant logic is less expressive than other non-classical logics.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Relevant logic differs from other non-classical logics primarily in its use of a different set of axioms.

Multiple choice

Which of the following is NOT a type of ambiguity?

  1. Lexical ambiguity

  2. Structural ambiguity

  3. Semantic ambiguity

  4. Anaphora
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Anaphora is a type of discourse relation, not a type of ambiguity. It refers to the use of a pronoun or other referring expression to refer back to a previously mentioned entity in the discourse.

Multiple choice

Which of the following is NOT a type of inference?

  1. Anaphora resolution

  2. Conversational implicature

  3. Presupposition

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

Anaphora resolution is a technique used in natural language processing to identify and resolve anaphoric references in a text. It is not a type of inference.