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

The following proposition is an example of a contradiction:

  1. (P ∧ ¬P)

  2. (P → Q) → ¬Q

  3. (P ∨ Q) ∧ (¬P ∨ ¬Q)

  4. (P ∧ Q) → P
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(P ∧ ¬P) is a contradiction because it is always false, regardless of the truth value of P.

Multiple choice

In propositional logic, a contingency is a compound proposition that is neither a tautology nor a contradiction.

  1. True

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

A contingency is a compound proposition that is neither a tautology nor a contradiction.

Multiple choice

The following proposition is an example of a contingency:

  1. (P ∨ ¬P)

  2. (P ∧ Q) → P

  3. (P → Q) → ¬Q

  4. (P ∨ Q) ∧ (¬P ∨ ¬Q)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

(P → Q) → ¬Q is a contingency because its truth value depends on the truth values of P and Q.

Multiple choice

The distributive law in propositional logic states that:

  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
B Correct answer
Explanation

The distributive law in propositional logic states that (P ∧ (Q ∨ R)) = (P ∧ Q) ∨ (P ∧ R).

Multiple choice

The associative law in propositional logic states that:

  1. (P ∨ (Q ∨ R)) = (P ∨ Q) ∨ R

  2. (P ∧ (Q ∧ R)) = (P ∧ Q) ∧ R

  3. (P → (Q → R)) = (P → Q) → R

  4. (P ∨ (Q → R)) = (P ∨ Q) → R
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The associative law in propositional logic states that (P ∧ (Q ∧ R)) = (P ∧ Q) ∧ R.

Multiple choice

The De Morgan's laws in propositional logic state that:

  1. ¬(P ∨ Q) = ¬P ∨ ¬Q and ¬(P ∧ Q) = ¬P ∧ ¬Q

  2. ¬(P → Q) = P ∨ ¬Q and ¬(P ∧ Q) = P ∨ ¬Q

  3. ¬(P → Q) = ¬P ∧ Q and ¬(P ∧ Q) = ¬P ∨ Q

  4. ¬(P → Q) = P ∧ ¬Q and ¬(P ∧ Q) = ¬P ∨ ¬Q
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

De Morgan's laws in propositional logic state that ¬(P ∨ Q) = ¬P ∨ ¬Q and ¬(P ∧ Q) = ¬P ∧ ¬Q.

Multiple choice

What is the Burali-Forti Paradox?

  1. A paradox in set theory that arises from the definition of the set of all sets.

  2. A paradox in set theory that arises from the definition of the set of all sets that contain themselves.

  3. A paradox in set theory that arises from the definition of the set of all sets that are not members of themselves.

  4. A paradox in set theory that arises from the definition of the set of all sets that do not contain themselves.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Burali-Forti Paradox is a paradox in set theory that arises from the definition of the set of all sets.

Multiple choice

Which reasoning technique is commonly used for non-monotonic reasoning in AI?

  1. Default Reasoning

  2. Circumscription

  3. Abduction

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

Default Reasoning, Circumscription, and Abduction are all commonly used reasoning techniques for non-monotonic reasoning in AI.

Multiple choice

Which of the following is an example of induction?

  1. All swans are white.

  2. The sun will rise tomorrow.

  3. The law of gravity is true.

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

All swans are white is an example of induction because it is a generalization from specific observations.

Multiple choice

Which of the following is an example of deduction?

  1. All swans are white.

  2. The sun will rise tomorrow.

  3. The law of gravity is true.

  4. God exists.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The law of gravity is true is an example of deduction because it is a conclusion that is drawn from general principles.

Multiple choice

What is the verification principle?

  1. A statement is meaningful if and only if it can be verified through sense experience.

  2. A statement is meaningful if and only if it is logically consistent.

  3. A statement is meaningful if and only if it is supported by evidence.

  4. A statement is meaningful if and only if it is expressed in clear and unambiguous language.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The verification principle is a central tenet of logical positivism. It states that a statement is meaningful if and only if it can be verified through sense experience.

Multiple choice

What is the name of Bertrand Russell's paradox?

  1. The Barber Paradox

  2. The Liar Paradox

  3. Russell's Paradox

  4. Zeno's Paradox
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Russell's Paradox is a logical paradox that arises from the concept of a set of all sets. It shows that the concept of a set of all sets is self-contradictory.

Multiple choice

According to Indian logic, what are the two main types of fallacies?

  1. Formal and informal

  2. Major and minor

  3. Deductive and inductive

  4. True and false
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to Indian logic, fallacies are classified into two main types: formal and informal. Formal fallacies are errors in the structure of an argument, while informal fallacies are errors in the content of an argument.

Multiple choice

What is an example of a formal fallacy?

  1. Ad hominem

  2. Begging the question

  3. Affirming the consequent

  4. Denying the antecedent
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Affirming the consequent is an example of a formal fallacy. It occurs when someone assumes that because the consequent of a conditional statement is true, the antecedent must also be true.

Multiple choice

What is an example of an informal fallacy?

  1. Ad hominem

  2. Begging the question

  3. Affirming the consequent

  4. Denying the antecedent
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ad hominem is an example of an informal fallacy. It occurs when someone attacks the person making an argument rather than the argument itself.