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 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.

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.