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 rule against asking hypothetical questions?

  1. A cross-examiner cannot ask a question that assumes facts that are not in evidence.

  2. A cross-examiner cannot ask a question that is speculative or conjectural.

  3. A cross-examiner cannot ask a question that is argumentative.

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

The rule against asking hypothetical questions prohibits a cross-examiner from asking a question that assumes facts that are not in evidence, a question that is speculative or conjectural, or a question that is argumentative.

Multiple choice

What is an undecidable problem?

  1. A problem that can be solved by an algorithm that always terminates.

  2. A problem that can be solved by an algorithm that sometimes terminates.

  3. A problem that can be solved by an algorithm that never terminates.

  4. A problem that cannot be solved by any algorithm.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

An undecidable problem is a problem that cannot be solved by any algorithm.

Multiple choice

What is the diagonalization argument?

  1. An argument that shows that there is no algorithm that can solve the halting problem.

  2. An argument that shows that there is no algorithm that can solve the Post's correspondence problem.

  3. An argument that shows that there is no algorithm that can solve the Busy Beaver problem.

  4. An argument that shows that there is no algorithm that can solve any undecidable problem.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The diagonalization argument is a powerful technique that can be used to prove that certain problems are undecidable.

Multiple choice

What is the incompleteness theorem?

  1. A theorem that states that every consistent axiomatic system is either incomplete or contradictory.

  2. A theorem that states that every axiomatic system is either complete or contradictory.

  3. A theorem that states that every consistent axiomatic system is either complete or undecidable.

  4. A theorem that states that every axiomatic system is either incomplete or undecidable.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The incompleteness theorem is a fundamental result in mathematical logic that shows that there are certain statements that cannot be proven or disproven within a given axiomatic system.

Multiple choice

What is the Gödel's incompleteness theorem?

  1. A theorem that states that every consistent axiomatic system is either incomplete or contradictory.

  2. A theorem that states that every axiomatic system is either complete or contradictory.

  3. A theorem that states that every consistent axiomatic system is either complete or undecidable.

  4. A theorem that states that every axiomatic system is either incomplete or undecidable.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Gödel's incompleteness theorem is a fundamental result in mathematical logic that shows that there are certain statements that cannot be proven or disproven within a given axiomatic system.

Multiple choice

What is the Turing's proof of the halting problem?

  1. A proof that shows that there is no algorithm that can solve the halting problem.

  2. A proof that shows that there is no algorithm that can solve the Post's correspondence problem.

  3. A proof that shows that there is no algorithm that can solve the Busy Beaver problem.

  4. A proof that shows that there is no algorithm that can solve any undecidable problem.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Turing's proof of the halting problem is a seminal result in computer science that shows that there is no algorithm that can solve the halting problem.

Multiple choice

Which rhetorical device is used to present a false dilemma by limiting the options to two extremes?

  1. False Dilemma

  2. Straw Man

  3. Ad Hominem

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

False Dilemma is a rhetorical device that is used to present a false dilemma by limiting the options to two extremes.

Multiple choice

Which rhetorical device is used to attack the person making the argument rather than the argument itself?

  1. Ad Hominem

  2. Straw Man

  3. Circular Argument

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

Ad Hominem is a rhetorical device that is used to attack the person making the argument rather than the argument itself.

Multiple choice

Which rhetorical device is used to present a logical argument based on evidence and reasoning?

  1. Logos

  2. Pathos

  3. Ethos

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

Logos is a rhetorical device that is used to present a logical argument based on evidence and reasoning.

Multiple choice

What is the Sorites Paradox?

  1. A paradox that arises when trying to define a vague concept by a series of small steps.

  2. A paradox that arises when trying to define a clear concept by a series of small steps.

  3. A paradox that arises when trying to define a vague concept by a series of large steps.

  4. A paradox that arises when trying to define a clear concept by a series of large steps.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Sorites Paradox is a paradox that arises when trying to define a vague concept by a series of small steps. The paradox is that, if we start with a clearly true statement and then make a series of small changes, we can eventually reach a statement that is clearly false. This raises the question of where the line is between true and false.

Multiple choice

What is an example of the Sorites Paradox?

  1. The paradox of the heap.

  2. The paradox of the bald man.

  3. The paradox of the grain of sand.

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

The paradox of the heap is a classic example of the Sorites Paradox. It asks the question: at what point does a collection of objects become a heap? If we start with a single object, it is clearly not a heap. If we add one more object, it is still not a heap. And so on. But at some point, we will reach a point where the collection of objects becomes a heap. The question is: where is that point?

Multiple choice

What is the term for a tentative explanation that can be tested through experimentation?

  1. Theory

  2. Hypothesis

  3. Law

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

A hypothesis is a tentative explanation that can be tested through experimentation.

Multiple choice

What are the three main types of proof?

  1. Direct proof, circumstantial proof, and demonstrative proof

  2. Direct proof, indirect proof, and rebuttable proof

  3. Direct proof, presumptive proof, and conclusive proof

  4. Direct proof, circumstantial proof, and testimonial proof
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The three main types of proof are direct proof, circumstantial proof, and demonstrative proof.

Multiple choice

Which of the following is a logically valid argument form?

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

  2. P or Q. Not P. Therefore, Q.

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

  4. P and Q. Therefore, P or Q.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This argument form is known as modus tollens and is logically valid because if the antecedent (P) is true and the consequent (Q) is false, then the negation of the antecedent (not P) must be true.

Multiple choice

What is the truth value of the following proposition: (P or Q) and (not P and not Q)?

  1. True

  2. False

  3. Indeterminate
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using a truth table, we can determine that the proposition is false in all possible cases.