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

What is the liar paradox?

  1. A paradox that arises from the statement 'This statement is false.'

  2. A paradox that arises from the statement 'I am lying.'

  3. A paradox that arises from the statement 'All statements are true.'

  4. A paradox that arises from the statement 'Nothing is true.'
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A Correct answer
Explanation

The liar paradox is a paradox that arises from the statement 'This statement is false.' If the statement is true, then it must be false, and if it is false, then it must be true. This leads to a contradiction.

Multiple choice

What is the T-schema, and how does it relate to Tarski's theory of truth?

  1. The T-schema is a schema that defines the truth conditions of a statement.

  2. The T-schema is a schema that defines the logical consequences of a statement.

  3. The T-schema is a schema that defines the syntactic structure of a statement.

  4. The T-schema is a schema that defines the semantic meaning of a statement.
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A Correct answer
Explanation

The T-schema is a schema that defines the truth conditions of a statement. It states that a statement 'p' is true if and only if 'p' is the case. In other words, the truth of a statement is determined by its correspondence to the facts of the world.

Multiple choice

What is the liar paradox, and how does it challenge our understanding of truth?

  1. The liar paradox is a paradox that arises from the statement 'This statement is false.'

  2. The liar paradox is a paradox that arises from the statement 'I am lying.'

  3. The liar paradox is a paradox that arises from the statement 'All statements are true.'

  4. The liar paradox is a paradox that arises from the statement 'Nothing is true.'
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A Correct answer
Explanation

The liar paradox is a paradox that arises from the statement 'This statement is false.' If the statement is true, then it must be false, and if it is false, then it must be true. This leads to a contradiction.

Multiple choice

Which of the following is a propositional connective?

  1. And

  2. Or

  3. Not

  4. All of the above
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Correct answer
Explanation

Propositional connectives are logical operators that connect propositions to form compound propositions.

Multiple choice

What is the truth value of the proposition "P and Q" when P is true and Q is false?

  1. True

  2. False

  3. Indeterminate
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Correct answer
Explanation

The truth value of a conjunction is true only when both conjuncts are true.

Multiple choice

What is the truth value of the proposition "P or Q" when P is false and Q is true?

  1. True

  2. False

  3. Indeterminate
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Correct answer
Explanation

The truth value of a disjunction is true when at least one disjunct is true.

Multiple choice

What is the truth value of the proposition "not P" when P is true?

  1. True

  2. False

  3. Indeterminate
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Correct answer
Explanation

The truth value of a negation is the opposite of the truth value of the negated proposition.

Multiple choice

Which of the following is an example of a conditional proposition?

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

  2. Either it is raining or the ground is wet.

  3. It is raining and the ground is wet.

  4. It is not raining.
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Correct answer
Explanation

A conditional proposition is a proposition that has the form "if P, then Q", where P is the antecedent and Q is the consequent.

Multiple choice

What is the truth value of the conditional proposition "If P, then Q" when P is true and Q is false?

  1. True

  2. False

  3. Indeterminate
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Correct answer
Explanation

The truth value of a conditional proposition is true when the antecedent is false or the consequent is true. In this case, the antecedent is true and the consequent is false, so the truth value of the proposition is false.

Multiple choice

What is the truth value of the biconditional proposition "P if and only if Q" when P is true and Q is true?

  1. True

  2. False

  3. Indeterminate
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Correct answer
Explanation

The truth value of a biconditional proposition is true when the antecedent and the consequent have the same truth value.

Multiple choice

Which of the following is an example of a tautology?

  1. P or not P

  2. P and not P

  3. If P, then P

  4. If P, then not P
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Correct answer
Explanation

A tautology is a proposition that is always true, regardless of the truth values of its component propositions.

Multiple choice

Which of the following is an example of a contradiction?

  1. P or not P

  2. P and not P

  3. If P, then P

  4. If P, then not P
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Correct answer
Explanation

A contradiction is a proposition that is always false, regardless of the truth values of its component propositions.

Multiple choice

What is the law of detachment?

  1. If P, then Q. Therefore, Q.

  2. If P, then Q. Therefore, not P.

  3. If P, then Q. Therefore, not Q.

  4. If P, then Q. Therefore, P.
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Correct answer
Explanation

The law of detachment is a rule of inference that allows us to conclude Q from P and the conditional proposition "If P, then Q".

Multiple choice

What is the law of syllogism?

  1. If P, then Q. If Q, then R. Therefore, P, then R.

  2. If P, then Q. If Q, then R. Therefore, Q, then R.

  3. If P, then Q. If Q, then R. Therefore, R, then P.

  4. If P, then Q. If Q, then R. Therefore, P, then Q.
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Correct answer
Explanation

The law of syllogism is a rule of inference that allows us to conclude P then R from P then Q and Q then R.

Multiple choice

What is the fallacy of affirming the consequent?

  1. If P, then Q. Q. Therefore, P.

  2. If P, then Q. Not P. Therefore, not Q.

  3. If P, then Q. Not Q. Therefore, P.

  4. If P, then Q. P. Therefore, Q.
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Correct answer
Explanation

The fallacy of affirming the consequent is the logical fallacy of concluding P from Q and the conditional proposition "If P, then Q".