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 tautology?

  1. $\lnot(p \wedge q) \rightarrow (\lnot p \vee \lnot q)$
  2. $\lnot(p \vee q) \rightarrow (\lnot p \wedge \lnot q)$
  3. $\lnot(p \rightarrow q) \rightarrow (p \wedge \lnot q)$
  4. $\lnot(p \leftrightarrow q) \rightarrow (p \wedge \lnot q)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A tautology is a propositional formula that is true for all possible combinations of truth values of its constituent propositions. In this case, the propositional formula "$\lnot(p \wedge q) \rightarrow (\lnot p \vee \lnot q)$" is a tautology because it is true for all possible combinations of truth values of "$p$" and "$q$".

Multiple choice

Which of the following is a modal logic operator?

  1. Necessity

  2. Possibility

  3. Obligation

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

Modal logic operators are operators that are used to express the necessity, possibility, obligation, or permission of propositions. In this case, the modal logic operator "Necessity" is used to express the necessity of a proposition.

Multiple choice

What is the term used to describe a statement that is assumed to be true without proof in a geometric system?

  1. Theorem

  2. Axiom

  3. Postulate

  4. Corollary
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

An axiom is a statement that is accepted as true without requiring proof. It serves as a fundamental building block for deducing other theorems and propositions within a geometric system.

Multiple choice

Which of the following is a logically valid argument form?

  1. Modus Ponens

  2. Affirming the Consequent

  3. Denying the Antecedent

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

Modus Ponens is a valid argument form where if P implies Q and P is true, then Q must also be true.

Multiple choice

What is the fallacy of affirming the consequent?

  1. Assuming the conclusion is true

  2. Reversing the order of the premises

  3. Denying the antecedent

  4. Drawing a conclusion from a false premise
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Affirming the consequent is the fallacy of assuming that if Q is true, then P must also be true, even though P implies Q does not guarantee the converse.

Multiple choice

Which of these statements is a tautology?

  1. P or not P

  2. P implies Q and Q implies P

  3. (P and Q) implies P

  4. P implies (Q or R)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A tautology is a statement that is always true, regardless of the truth values of its components. 'P or not P' is a tautology because either P is true or not P is true, making the statement always true.

Multiple choice

What is the rule of detachment in propositional logic?

  1. If P implies Q and P is true, then Q is true

  2. If P implies Q and Q is false, then P is false

  3. If P and Q are both true, then P implies Q

  4. If P is false, then not P is true
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The rule of detachment states that if you have a conditional statement (P implies Q) and you know that the antecedent (P) is true, then you can conclude that the consequent (Q) is also true.

Multiple choice

Which of the following is an example of a deductively valid argument?

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

  2. Some birds can fly. Tweety is a bird. Therefore, Tweety can fly.

  3. All cats have fur. Mittens is a cat. Therefore, Mittens has scales.

  4. Some flowers are red. Roses are flowers. Therefore, all roses are red.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A deductively valid argument is one where the conclusion follows logically from the premises. In this case, the premises 'All dogs are mammals' and 'Fido is a dog' logically imply the conclusion 'Fido is a mammal'.

Multiple choice

What is the fallacy of denying the antecedent?

  1. Assuming the consequent is true

  2. Reversing the order of the premises

  3. Denying the consequent

  4. Drawing a conclusion from a false premise
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

Denying the antecedent is the fallacy of assuming that if P implies Q and P is false, then Q must also be false. However, this is not necessarily the case.

Multiple choice

Which of these statements is a contradiction?

  1. P and not P

  2. P implies Q and Q implies P

  3. (P and Q) implies P

  4. P implies (Q or R)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A contradiction is a statement that is always false, regardless of the truth values of its components. 'P and not P' is a contradiction because it is impossible for both P and not P to be true at the same time.

Multiple choice

What is the principle of explosion in propositional logic?

  1. If P is false, then anything can be inferred

  2. If P implies Q and Q is false, then P is false

  3. If P and Q are both true, then P implies Q

  4. If P is true, then not P is false
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The principle of explosion states that if a statement is false, then any other statement can be inferred from it. This is because a false statement has no logical constraints, so anything can be derived from it.

Multiple choice

Which of the following is an example of a deductively invalid argument?

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

  2. Some birds can fly. Tweety is a bird. Therefore, Tweety can fly.

  3. All cats have fur. Mittens is a cat. Therefore, Mittens has scales.

  4. Some flowers are red. Roses are flowers. Therefore, all roses are red.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A deductively invalid argument is one where the conclusion does not necessarily follow from the premises. In this case, the premises 'All dogs are mammals' and 'Fido is a mammal' do not logically imply the conclusion 'Fido is a dog'.

Multiple choice

What is the fallacy of the undistributed middle term?

  1. Assuming the conclusion is true

  2. Reversing the order of the premises

  3. Using a term in both premises but not distributing it

  4. Drawing a conclusion from a false premise
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The fallacy of the undistributed middle term occurs when a term appears in both premises of a syllogism but is not distributed in at least one of them. This can lead to an invalid argument.

Multiple choice

Which of these statements is a contingency?

  1. P or not P

  2. P implies Q and Q implies P

  3. (P and Q) implies P

  4. P implies (Q or R)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A contingency is a statement that is neither a tautology nor a contradiction. Its truth value depends on the truth values of its components. 'P implies (Q or R)' is a contingency because its truth value depends on the truth values of P, Q, and R.

Multiple choice

What is the rule of substitution in propositional logic?

  1. If P implies Q and R is equivalent to P, then Q implies R

  2. If P implies Q and Q implies R, then P implies R

  3. If P and Q are both true, then P implies Q

  4. If P is false, then not P is true
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The rule of substitution states that if you have a conditional statement (P implies Q) and you know that R is equivalent to P, then you can substitute R for P in the conditional statement to get (R implies Q).