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 an example of a sound argument?

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

  2. The ground is wet, therefore it is raining.

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

  4. It is raining, therefore the ground is wet.
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

A sound argument is an argument that is both valid and has true premises. In this case, the argument is valid because the conclusion follows logically from the premises. The premises are also true, because it is a fact that if it is raining, then the ground will be wet. Therefore, the argument is sound.

Multiple choice

Which of the following is an example of an unsound argument?

  1. All men are mortal.

  2. Socrates is a man.

  3. Therefore, Socrates is mortal.

  4. All men are mortal.

  5. Socrates is a man.
Reveal answer Fill a bubble to check yourself
A,D Correct answer
Explanation

An unsound argument is an argument that is either invalid or has false premises. In this case, the argument is invalid because the conclusion does not follow logically from the premises. The premises are also false, because it is not true that all men are mortal. Therefore, the argument is unsound.

Multiple choice

Which of the following is an example of a formal fallacy?

  1. Affirming the consequent

  2. Denying the antecedent

  3. Modus ponens

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

A formal fallacy is a fallacy that is based on the structure of the argument, rather than the content of the premises. Affirming the consequent is a formal fallacy in which the conclusion is drawn that P must be true because Q is true. However, this is not necessarily the case. For example, if we know that "If it is raining, then the ground is wet", we cannot conclude that "The ground is wet, therefore it is raining."

Multiple choice

Which of the following is an example of an informal fallacy?

  1. Ad hominem

  2. Ad populum

  3. Straw man

  4. Begging the question
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

An informal fallacy is a fallacy that is based on the content of the premises, rather than the structure of the argument. Ad hominem is an informal fallacy in which the speaker attacks the person making the argument, rather than the argument itself. For example, if someone says "You can't trust what he says because he's a liar", they are committing the ad hominem fallacy.

Multiple choice

Which logical connective is used to represent the logical operation of "and"?

  1. ∧

  2. ∨

  3. ¬

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

The logical connective ∧ (also known as conjunction) is used to represent the logical operation of "and". It is typically used to combine two or more propositions into a single compound proposition, and the resulting proposition is true only if all of the individual propositions are true.

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 connectives, we can evaluate the truth value of the proposition. When P is true, Q is false, and R is true, the truth value of (P ∨ Q) is true, and the truth value of ¬R is false. Therefore, the truth value of the entire proposition is false.

Multiple choice

Which of the following is a valid logical argument?

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

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

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

A valid logical argument is one in which the conclusion follows logically from the premises. In the first option, the conclusion follows logically from the premises, so it is a valid argument. The other two options are not valid because the conclusions do not follow logically from the premises.

Multiple choice

Which of the following is a tautology?

  1. (P ∨ ¬P)

  2. (P ∧ ¬P)

  3. (P → Q) ∧ (Q → P)

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

A tautology is a proposition that is always true, regardless of the truth values of its component propositions. (P ∨ ¬P) is a tautology because it is always true: either P is true or ¬P is true, or both.

Multiple choice

What is the truth value of the proposition "(P → Q) ∧ (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 connectives, we can evaluate the truth value of the proposition. When P is true, Q is false, and R is true, the truth value of (P → Q) is false, and the truth value of (Q → R) is true. Therefore, the truth value of the entire proposition is false.

Multiple choice

Which of the following is a fallacy?

  1. Affirming the consequent

  2. Denying the antecedent

  3. Modus ponens

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

Affirming the consequent is a fallacy in which the conclusion of a conditional statement is assumed to be true, and therefore the antecedent must also be true. It is a logical fallacy because the truth of the consequent does not necessarily imply the truth of the antecedent.

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
A Correct answer
Explanation

Using the truth table for logical connectives, we can evaluate the truth value of the proposition. When P is true, Q is false, and R is true, the truth value of (P ∧ Q) is false, and the truth value of (P ∧ Q) → R is true. Therefore, the truth value of the entire proposition is true.

Multiple choice

Which of the following is a valid logical argument?

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

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

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

A valid logical argument is one in which the conclusion follows logically from the premises. In the first option, the conclusion follows logically from the premises, so it is a valid argument. The other two options are not valid because the conclusions do not follow logically from the premises.

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 connectives, we can evaluate the truth value of the proposition. When P is true, Q is false, and R is true, the truth value of (P ∨ Q) is true, and the truth value of ¬R is false. Therefore, the truth value of the entire proposition is false.

Multiple choice

Which of the following is a tautology?

  1. (P ∨ ¬P)

  2. (P ∧ ¬P)

  3. (P → Q) ∧ (Q → P)

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

A tautology is a proposition that is always true, regardless of the truth values of its component propositions. (P ∨ ¬P) is a tautology because it is always true: either P is true or ¬P is true, or both.

Multiple choice

What is the truth value of the proposition "(P → Q) ∧ (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 connectives, we can evaluate the truth value of the proposition. When P is true, Q is false, and R is true, the truth value of (P → Q) is false, and the truth value of (Q → R) is true. Therefore, the truth value of the entire proposition is false.