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 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 that occurs when we infer the truth of the antecedent from the truth of the consequent. For example, if we have the conditional statement If P, then Q and we know that Q is true, we cannot conclude that P is also true. This is because there may be other conditions that can also lead to Q being true.

Multiple choice

Which of the following is a valid argument form for universal generalization?

  1. For all x, P(x).

  2. P(a).

  3. Therefore, for all x, P(x).

  4. P(a), therefore P(b).
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

Universal generalization is a rule of inference that allows us to infer the conclusion For all x, P(x) from the premises For all x, P(x) and P(a), where a is an arbitrary member of the domain of discourse. In the given argument form, we have the premise For all x, P(x) and the premise P(a). Therefore, we can infer the conclusion For all x, P(x).

Multiple choice

Which of the following is a valid argument form for existential generalization?

  1. There exists an x such that P(x).

  2. P(a).

  3. Therefore, there exists an x such that P(x).

  4. P(a), therefore P(b).
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

Existential generalization is a rule of inference that allows us to infer the conclusion There exists an x such that P(x) from the premises There exists an x such that P(x) and P(a), where a is an arbitrary member of the domain of discourse. In the given argument form, we have the premise There exists an x such that P(x) and the premise P(a). Therefore, we can infer the conclusion There exists an x such that P(x).

Multiple choice

Which of the following is a valid argument form for universal instantiation?

  1. For all x, P(x).

  2. a is an arbitrary member of the domain of discourse.

  3. Therefore, P(a).

  4. P(a), therefore P(b).
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

Universal instantiation is a rule of inference that allows us to infer the conclusion P(a) from the premises For all x, P(x) and a is an arbitrary member of the domain of discourse. In the given argument form, we have the premise For all x, P(x) and the premise a is an arbitrary member of the domain of discourse. Therefore, we can infer the conclusion P(a).

Multiple choice

Which of the following is a valid argument form for existential instantiation?

  1. There exists an x such that P(x).

  2. a is an arbitrary member of the domain of discourse.

  3. Therefore, P(a).

  4. P(a), therefore P(b).
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

Existential instantiation is a rule of inference that allows us to infer the conclusion P(a) from the premises There exists an x such that P(x) and a is an arbitrary member of the domain of discourse. In the given argument form, we have the premise There exists an x such that P(x) and the premise a is an arbitrary member of the domain of discourse. Therefore, we can infer the conclusion P(a).

Multiple choice

Which of the following is a valid argument form for hypothetical syllogism?

  1. If P, then Q.

  2. If Q, then R.

  3. Therefore, if P, then R.

  4. P, therefore Q.
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

Hypothetical syllogism is a rule of inference that allows us to infer the conclusion If P, then R from the premises If P, then Q and If Q, then R. In the given argument form, we have the premises If P, then Q and If Q, then R. Therefore, we can infer the conclusion If P, then R.

Multiple choice

Which of the following is a valid argument form for disjunctive syllogism?

  1. P or Q.

  2. Not P.

  3. Therefore, Q.

  4. P, therefore Q.
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

Disjunctive syllogism is a rule of inference that allows us to infer the conclusion Q from the premises P or Q and Not P. In the given argument form, we have the premises P or Q and Not P. Therefore, we can infer the conclusion Q.

Multiple choice

Which of the following is a valid argument form for constructive dilemma?

  1. Either P or Q.

  2. If P, then R.

  3. If Q, then S.

  4. Therefore, either R or S.

  5. P, therefore Q.
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

Constructive dilemma is a rule of inference that allows us to infer the conclusion Either R or S from the premises Either P or Q, If P, then R, and If Q, then S. In the given argument form, we have the premises Either P or Q, If P, then R, and If Q, then S. Therefore, we can infer the conclusion Either R or S.

Multiple choice

Which of the following is a valid argument form for destructive dilemma?

  1. Either P or Q.

  2. If P, then R.

  3. If Q, then S.

  4. Not R.

  5. Therefore, not Q.

  6. P, therefore Q.
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

Destructive dilemma is a rule of inference that allows us to infer the conclusion Not Q from the premises Either P or Q, If P, then R, If Q, then S, and Not R. In the given argument form, we have the premises Either P or Q, If P, then R, If Q, then S, and Not R. Therefore, we can infer the conclusion Not Q.

Multiple choice

Which of the following is a negation in the statement "It is not true that the Earth is flat"?

  1. It is not true

  2. That the Earth is flat
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A negation is a statement that denies the truth of another statement. In this case, the negation is "It is not true", which denies the truth of the statement "The Earth is flat".

Multiple choice

What is the principle of non-contradiction?

  1. It is impossible for a proposition to be both true and false at the same time and in the same respect.

  2. It is impossible for a proposition to be true and false at different times.

  3. It is impossible for a proposition to be true and false in different respects.

  4. It is impossible for a proposition to be true and false in different contexts.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The principle of non-contradiction states that it is impossible for a proposition to be both true and false at the same time and in the same respect. This principle is considered a fundamental law of logic and is essential for rational thought.

Multiple choice

Which of the following is a necessary condition for a causal explanation to be complete?

  1. The explanation must identify the cause of the event.

  2. The explanation must identify all of the factors that contribute to the event.

  3. The explanation must show how the cause produces the effect.

  4. The explanation must be logically valid.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A causal explanation is an explanation that identifies the cause of an event. Therefore, a necessary condition for a causal explanation to be complete is that it must show how the cause produces the effect.

Multiple choice

Which of the following is a necessary condition for a causal explanation to be satisfactory?

  1. The explanation must identify the cause of the event.

  2. The explanation must identify all of the factors that contribute to the event.

  3. The explanation must show how the cause produces the effect.

  4. The explanation must be logically valid.
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

A causal explanation is an explanation that identifies the cause of an event. Therefore, a necessary condition for a causal explanation to be satisfactory is that it must be satisfactory to the person who is seeking the explanation.

Multiple choice

Which of the following is a necessary condition for a causal explanation to be true?

  1. The explanation must identify the cause of the event.

  2. The explanation must identify all of the factors that contribute to the event.

  3. The explanation must show how the cause produces the effect.

  4. The explanation must be logically valid.
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

A causal explanation is an explanation that identifies the cause of an event. Therefore, a necessary condition for a causal explanation to be true is that it must be true.

Multiple choice

Which of the following is a valid argument form?

  1. Modus Ponens

  2. Modus Tollens

  3. Hypothetical Syllogism

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

Modus Ponens, Modus Tollens, and Hypothetical Syllogism are all valid argument forms in propositional logic.