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

In the context of mathematics and metaphysics, what does the term 'axioms' refer to?

  1. Self-evident truths that serve as the foundation for mathematical reasoning

  2. Arbitrary statements that are assumed to be true for the sake of mathematical exploration

  3. Mathematical propositions that can be derived from other axioms or theorems

  4. Complex mathematical equations that describe physical phenomena
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Axioms are fundamental statements in mathematics that are considered to be self-evidently true and serve as the basis for deductive reasoning.

Multiple choice

Which mathematical principle asserts that every mathematical statement can be either proven or disproven?

  1. The Law of Excluded Middle

  2. The Law of Non-Contradiction

  3. The Axiom of Choice

  4. The Completeness Theorem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Law of Excluded Middle states that for any proposition, either it or its negation is true, allowing for a binary division of truth values.

Multiple choice

Which theory of truth states that the truth of a statement is determined by its coherence with other statements in a system?

  1. Correspondence Theory

  2. Coherence Theory

  3. Pragmatic Theory

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

The Coherence Theory of Truth states that the truth of a statement is determined by its coherence with other statements in a system. This means that a statement is true if it is consistent with the other statements in the system and does not lead to any contradictions.

Multiple choice

In hypothesis testing, what is the probability of rejecting the null hypothesis when it is actually true?

  1. Type I error

  2. Type II error

  3. Significance level

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

Type I error is the probability of rejecting the null hypothesis when it is actually true. It is also known as the false positive rate.

Multiple choice

Which of the following is NOT a type of legal argument?

  1. Deductive argument

  2. Inductive argument

  3. Analogical argument

  4. Emotional argument
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Emotional argument is not a type of legal argument, as it is based on emotion rather than logic.

Multiple choice

What is a hypothesis?

  1. A proposed explanation for a phenomenon

  2. A prediction about the outcome of an experiment

  3. A statement of fact

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

A hypothesis is a proposed explanation for a phenomenon. It is based on observations and evidence, and it can be tested through experimentation.

Multiple choice

Which of the following is an example of a belief that is not based on evidence?

  1. I believe that the Earth is round.

  2. I believe that God exists.

  3. I believe that the stock market will go up tomorrow.

  4. I believe that my favorite sports team will win the championship.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A belief that is not based on evidence is one that is not supported by any facts or observations. In this case, the belief that God exists is not based on evidence, as there is no scientific evidence to support it.

Multiple choice

Which of the following is an example of an opinion?

  1. I believe that the Earth is round.

  2. I believe that God exists.

  3. I believe that the stock market will go up tomorrow.

  4. I believe that my favorite sports team will win the championship.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

An opinion is something that is thought to be true, but is not based on evidence. In this case, the belief that my favorite sports team will win the championship is an opinion, as it is not based on any evidence.

Multiple choice

Which of the following is an example of understanding?

  1. I know that the Earth is round.

  2. I know that God exists.

  3. I know that the stock market will go up tomorrow.

  4. I know that my favorite sports team will win the championship.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Understanding is the ability to grasp the meaning of information and see how it fits together. In this case, the statement "I know that the Earth is round" demonstrates understanding, as it shows that the person understands the concept of the Earth being round and its implications.

Multiple choice

Which of the following is a valid Boolean expression?

  1. A ∧ B ∨ C

  2. A ∨ B ∧ C

  3. A ⊕ B ∧ C

  4. A ⊕ B ∨ C
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In Boolean algebra, the order of operations is important. Parentheses can be used to group expressions and ensure that they are evaluated in the correct order.

Multiple choice

What is the dual of the expression A ∨ B?

  1. A ∧ B

  2. ¬A ∧ ¬B

  3. ¬A ∨ ¬B

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

The dual of a Boolean expression is obtained by interchanging ∧ and ∨, and 0 and 1.

Multiple choice

Which of the following is a tautology?

  1. A ∨ ¬A

  2. A ∧ ¬A

  3. A ⊕ ¬A

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

A tautology is a Boolean expression that is always true, regardless of the values of its variables.

Multiple choice

What is the complement of the expression A ∧ B?

  1. ¬A ∨ ¬B

  2. ¬A ∧ ¬B

  3. A ∨ B

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

The complement of a Boolean expression is the expression that is true when the original expression is false, and vice versa.

Multiple choice

What is the complement of the expression A ∨ B?

  1. ¬A ∧ ¬B

  2. ¬A ∨ ¬B

  3. A ∧ B

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

The complement of a Boolean expression is the expression that is true when the original expression is false, and vice versa.

Multiple choice

What is the De Morgan's law in Boolean algebra?

  1. ¬(A ∧ B) = ¬A ∨ ¬B

  2. ¬(A ∨ B) = ¬A ∧ ¬B

  3. ¬(A ⊕ B) = ¬A ⊕ ¬B

  4. ¬(A ∧ B) = ¬A ⊕ ¬B
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

De Morgan's law states that the negation of a conjunction is the disjunction of the negations, and vice versa.