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

Which of the following is an example of a hypothetical syllogism?

  1. If it is raining, then the ground is wet.

  2. All dogs are mammals.

  3. Either it is raining or it is snowing.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A hypothetical syllogism is a type of logical argument that consists of a conditional statement (the "if-then" statement) and a categorical statement (the "then" statement).

Multiple choice

Which of the following is an example of a disjunctive syllogism?

  1. Either it is raining or it is snowing.

  2. If it is raining, then the ground is wet.

  3. All dogs are mammals.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A disjunctive syllogism is a type of logical argument that consists of a disjunction (an "either-or" statement) and a categorical statement.

Multiple choice

What is the contrapositive of the proposition "If it is raining, then the ground is wet."?

  1. If the ground is not wet, then it is not raining.

  2. If it is not raining, then the ground is not wet.

  3. If the ground is wet, then it is raining.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The contrapositive of a proposition is formed by negating both the hypothesis and the conclusion.

Multiple choice

Which of the following is an example of a categorical syllogism?

  1. If it is raining, then the ground is wet.

  2. All dogs are mammals.

  3. Either it is raining or it is snowing.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A categorical syllogism is a type of logical argument that consists of two categorical statements (statements that make a claim about all or some members of a class).

Multiple choice

What is the truth value of the proposition "$(p \wedge q) \rightarrow (p \vee q)$"?

  1. True

  2. False

  3. Indeterminate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The proposition "$(p \wedge q) \rightarrow (p \vee q)$" is a tautology, meaning it is always true.

Multiple choice

Which of the following is an example of a modus ponens argument?

  1. If it is raining, then the ground is wet. It is raining. Therefore, the ground is wet.

  2. All dogs are mammals. Fido is a dog. Therefore, Fido is a mammal.

  3. Either it is raining or it is snowing. It is not raining. Therefore, it is snowing.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A modus ponens argument is a type of logical argument that consists of a conditional statement (the "if-then" statement) and a categorical statement (the "then" statement).

Multiple choice

What is the truth value of the proposition "$p \rightarrow (q \wedge r)$"?

  1. True

  2. False

  3. Indeterminate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The proposition "$p \rightarrow (q \wedge r)$" is a tautology, meaning it is always true.

Multiple choice

Which of the following is an example of a modus tollens argument?

  1. If it is raining, then the ground is wet. The ground is not wet. Therefore, it is not raining.

  2. All dogs are mammals. Fido is not a mammal. Therefore, Fido is not a dog.

  3. Either it is raining or it is snowing. It is not snowing. Therefore, it is raining.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A modus tollens argument is a type of logical argument that consists of a conditional statement (the "if-then" statement) and a categorical statement that negates the conclusion of the conditional statement.

Multiple choice

What is the truth value of the proposition "$(p \vee q) \rightarrow (p \wedge q)$"?

  1. True

  2. False

  3. Indeterminate
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The proposition "$(p \vee q) \rightarrow (p \wedge q)$" is a fallacy, meaning it is not always true.

Multiple choice

Which of the following is an example of a hypothetical syllogism with a false conclusion?

  1. If it is raining, then the ground is wet. It is raining. Therefore, the ground is wet.

  2. All dogs are mammals. Fido is a dog. Therefore, Fido is a mammal.

  3. If it is raining, then the ground is wet. The ground is dry. Therefore, it is not raining.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The conclusion of this syllogism is false because the ground can be dry even if it is not raining.

Multiple choice

What is the truth value of the proposition "$((p \wedge q) \vee r) \rightarrow (p \vee (q \vee r))$"?

  1. True

  2. False

  3. Indeterminate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The proposition "$((p \wedge q) \vee r) \rightarrow (p \vee (q \vee r))$" is a tautology, meaning it is always true.

Multiple choice

Which of the following is an example of a disjunctive syllogism with a false conclusion?

  1. Either it is raining or it is snowing. It is raining. Therefore, it is not snowing.

  2. All dogs are mammals. Fido is a dog. Therefore, Fido is a mammal.

  3. Either it is raining or it is snowing. It is sunny. Therefore, it is not raining and it is not snowing.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The conclusion of this syllogism is false because it is possible for it to be sunny and raining or sunny and snowing.

Multiple choice

What is the truth value of the proposition "$(p \rightarrow q) \rightarrow ((\neg p) \vee q)$"?

  1. True

  2. False

  3. Indeterminate
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The proposition "$(p \rightarrow q) \rightarrow ((\neg p) \vee q)$" is a tautology, meaning it is always true.

Multiple choice

What are the three main types of opinion evidence?

  1. Lay opinion evidence, expert opinion evidence, and character evidence.

  2. Lay opinion evidence, expert opinion evidence, and hearsay evidence.

  3. Lay opinion evidence, expert opinion evidence, and real evidence.

  4. Lay opinion evidence, expert opinion evidence, and demonstrative evidence.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The three main types of opinion evidence are lay opinion evidence, expert opinion evidence, and character evidence.

Multiple choice

Which of the following is a tautology?

  1. ~(p ∨ q) ∨ (~p ∧ ~q)

  2. (p ∧ q) → (p ∨ q)

  3. ~p → (q → p)

  4. p ∨ ~p
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A tautology is a propositional formula that is always true, regardless of the truth values of its component propositions. In this case, the propositional formula "p ∨ ~p" is always true because it states that either "p" is true or "not p" is true, which is always the case.