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

What is the formula for the rule of instantiation for belief?

  1. $ \vdash B\forall x \phi \rightarrow B\phi [t/x] $
  2. $ \vdash B\phi [t/x] \rightarrow B\forall x \phi $
  3. $ \vdash \Diamond B\phi \rightarrow B\phi $
  4. $ \vdash B\phi \rightarrow \Diamond B\phi $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The rule of instantiation for belief states that if an agent believes a universal generalization, then the agent believes the instance of that generalization obtained by substituting any term for the variable.

Multiple choice

What is the formula for the rule of modus ponens for belief?

  1. $ \vdash B(\phi \rightarrow \psi) \wedge B\phi \rightarrow B\psi $
  2. $ \vdash B(\phi \rightarrow \psi) \wedge B\psi \rightarrow B\phi $
  3. $ \vdash \Diamond B\phi \rightarrow B\phi $
  4. $ \vdash B\phi \rightarrow \Diamond B\phi $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The rule of modus ponens for belief states that if an agent believes a conditional proposition and the antecedent of that proposition, then the agent believes the consequent of that proposition.

Multiple choice

What are some examples of the principle of identity?

  1. A book is a book.

  2. A tree is a tree.

  3. A person is a person.

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

The principle of identity states that everything is identical to itself. This means that a book is a book, a tree is a tree, and a person is a person.

Multiple choice

What is the opposite of the principle of identity?

  1. The principle of contradiction

  2. The principle of the excluded middle

  3. The principle of non-identity

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The opposite of the principle of identity is the principle of non-identity. The principle of non-identity states that something can be both itself and something else at the same time and in the same respect.

Multiple choice

Which of the following is a central concept in epistemic logic?

  1. Knowledge operator

  2. Belief operator

  3. Common knowledge operator

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

Epistemic logic uses various operators to represent knowledge, belief, and common knowledge.

Multiple choice

What is the common knowledge operator in epistemic logic?

  1. C

  2. K

  3. B

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

The common knowledge operator in epistemic logic is typically denoted by 'C'.

Multiple choice

What is the principle of non-contradiction?

  1. A statement cannot be both true and false at the same time and in the same sense.

  2. A statement can be both true and false at the same time and in the same sense.

  3. A statement can be true in one sense and false in another sense.

  4. A statement can be true in one context and false in another context.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The principle of non-contradiction states that a statement cannot be both true and false at the same time and in the same sense. This means that if a statement is true, then it cannot also be false, and vice versa.

Multiple choice

What is the logical symbol for the principle of non-contradiction?

  1. ¬(A ∧ ¬A)

  2. A ∨ ¬A

  3. A → ¬A

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

The logical symbol for the principle of non-contradiction is ¬(A ∧ ¬A), which means "not (A and not A)".

Multiple choice

What is the principle of non-contradiction sometimes called?

  1. The Law of Contradiction

  2. The Law of Excluded Middle

  3. The Law of Identity

  4. The Law of Sufficient Reason
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The principle of non-contradiction is sometimes called the Law of Contradiction.

Multiple choice

What is the opposite of the principle of non-contradiction?

  1. The principle of contradiction

  2. The principle of excluded middle

  3. The principle of identity

  4. The principle of sufficient reason
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The opposite of the principle of non-contradiction is the principle of contradiction, which states that a statement can be both true and false at the same time and in the same sense.

Multiple choice

What is one example of a statement that violates the principle of non-contradiction?

  1. The sky is blue.

  2. The grass is green.

  3. The sun is hot.

  4. A square circle exists.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A square circle exists is an example of a statement that violates the principle of non-contradiction because it is a statement that is both true and false at the same time and in the same sense. A square is a shape with four straight sides and four right angles, while a circle is a shape with no sides and no angles. Therefore, a square circle cannot exist.

Multiple choice

What is the principle of non-contradiction based on?

  1. The law of identity

  2. The law of excluded middle

  3. The law of sufficient reason

  4. The law of causality
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The principle of non-contradiction is based on the law of identity, which states that a thing is what it is. This means that a statement cannot be both true and false at the same time and in the same sense because a thing cannot be both itself and not itself at the same time and in the same sense.

Multiple choice

Which of the following is an example of a paradox?

  1. A character who is trying to escape from his past but is constantly haunted by it

  2. A character who is trying to achieve a goal but is constantly thwarted by obstacles

  3. A character who is trying to find love but is constantly rejected

  4. A statement that is both true and false at the same time
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A paradox is a statement that is both true and false at the same time. This can be a difficult concept to understand, but it is often used in literature to create a sense of mystery or wonder.

Multiple choice

Which of the following is a paradox that arises from the idea that truth is a property of statements?

  1. The liar's paradox

  2. The sorites paradox

  3. The Münchhausen trilemma

  4. The Euthyphro dilemma
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The liar's paradox is a paradox that arises from the idea that truth is a property of statements. The paradox is that if a statement says that it is false, then it is both true and false at the same time.

Multiple choice

Which of the following is a paradox that arises from the idea that truth is a property of beliefs?

  1. The liar's paradox

  2. The sorites paradox

  3. The Münchhausen trilemma

  4. The Euthyphro dilemma
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The Münchhausen trilemma is a paradox that arises from the idea that truth is a property of beliefs. The paradox is that if a belief is justified by another belief, then that belief must also be justified by another belief, and so on. This leads to an infinite regress of justification.