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 an example of a necessary truth?

  1. The sky is blue.

  2. The grass is green.

  3. The sun is hot.

  4. 2 + 2 = 4.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

2 + 2 = 4 is an example of a necessary truth because it is true in all possible worlds.

Multiple choice

Which of the following is an example of a contingent truth?

  1. The sky is blue.

  2. The grass is green.

  3. The sun is hot.

  4. 2 + 2 = 4.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sky is blue is an example of a contingent truth because it is not true in all possible worlds.

Multiple choice

Which of the following is an example of a possible world?

  1. A world where the sky is green and the grass is blue.

  2. A world where 2 + 2 = 5.

  3. A world where time travel is possible.

  4. A world where God does not exist.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A world where the sky is green and the grass is blue is an example of a possible world because it is not contradictory.

Multiple choice

Which of the following is an example of an impossible world?

  1. A world where the sky is green and the grass is blue.

  2. A world where 2 + 2 = 5.

  3. A world where time travel is possible.

  4. A world where God does not exist.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A world where 2 + 2 = 5 is an example of an impossible world because it is contradictory.

Multiple choice

What is the internal logic of a topos?

  1. The first-order logic of the topos

  2. The second-order logic of the topos

  3. The infinitary logic of the topos

  4. The intuitionistic logic of the topos
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The internal logic of a topos is the intuitionistic logic of the topos.

Multiple choice

What is the argument from self-refutation?

  1. The argument from contradiction

  2. The argument from self-refutation

  3. The argument from infinite regress

  4. The argument from common sense
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The argument from self-refutation states that if relativism is true, then there can be no objective truth about relativism itself. However, this is a contradiction, because the statement 'relativism is true' is itself a statement about relativism. Therefore, relativism cannot be true.

Multiple choice

What is the argument from infinite regress?

  1. The argument from contradiction

  2. The argument from self-refutation

  3. The argument from infinite regress

  4. The argument from common sense
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The argument from infinite regress states that if relativism is true, then there can be no objective truth about anything. This is because, for any statement $S$, we can always ask the question 'is $S$ true?' If relativism is true, then the answer to this question will be relative to the individual or group that is asked. However, this means that there can be no objective truth about whether or not $S$ is true. This leads to an infinite regress, because we can always ask the question 'is the answer to the question 'is $S$ true?' true?' And so on. Therefore, relativism cannot be true.

Multiple choice

What is the argument from common sense?

  1. The argument from contradiction

  2. The argument from self-refutation

  3. The argument from infinite regress

  4. The argument from common sense
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The argument from common sense states that relativism is simply not plausible. It is simply common sense that there are some truths that are objective and that are not relative to the individual or group that holds them. For example, it is a common sense truth that 2 + 2 = 4. This is a truth that is not relative to the individual or group that holds it. It is a truth that is true for everyone, regardless of their culture, beliefs, or values.

Multiple choice

Which of the following is an example of a concrete entity?

  1. A mathematical theorem

  2. A physical object, such as a chair

  3. A moral principle, such as honesty

  4. A mental state, such as a belief
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Concrete entities are tangible, particular, and dependent on time and space. A physical object, like a chair, falls into this category as it possesses these characteristics.

Multiple choice

Which of the following is an example of an abstract-concrete distinction?

  1. The distinction between a physical object and its properties

  2. The distinction between a mathematical concept and its applications

  3. The distinction between a moral principle and its consequences

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

Abstract-concrete distinctions involve the separation of abstract entities, such as concepts or principles, from their concrete manifestations or applications.

Multiple choice

Which logical connective is used to represent the "and" operation in Predicate Logic?

  1. \(\wedge\)
  2. \(\vee\)
  3. \(\neg\)
  4. \(\rightarrow\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The logical connective (\wedge) is used to represent the "and" operation in Predicate Logic. It is also known as the conjunction operator.

Multiple choice

What is the purpose of the universal quantifier (\forall) in Predicate Logic?

  1. To indicate that a statement holds for all elements in a domain

  2. To indicate that a statement holds for some elements in a domain

  3. To negate a statement

  4. To imply a statement
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The universal quantifier (\forall) is used to indicate that a statement holds for all elements in a domain. It is also known as the "for all" quantifier.

Multiple choice

Which of the following is an example of a valid argument in Predicate Logic?

  1. \(\forall x \in \mathbb{R}, x^2 \ge 0\)
  2. \(\exists x \in \mathbb{R}, x^2 < 0\)
  3. \(\neg \forall x \in \mathbb{R}, x^2 \ge 0\)
  4. \(\exists x \in \mathbb{R}, x^2 = -1\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The argument (\forall x \in \mathbb{R}, x^2 \ge 0) is a valid argument in Predicate Logic because it is true for all values of (x) in the domain (\mathbb{R}).

Multiple choice

What is the difference between a propositional variable and a predicate variable in Predicate Logic?

  1. Propositional variables represent statements, while predicate variables represent properties

  2. Propositional variables can be true or false, while predicate variables can be true, false, or undefined

  3. Propositional variables are used to form compound propositions, while predicate variables are used to form predicates

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

All of the above statements are true. Propositional variables represent statements, while predicate variables represent properties. Propositional variables can be true or false, while predicate variables can be true, false, or undefined. Propositional variables are used to form compound propositions, while predicate variables are used to form predicates.

Multiple choice

Which of the following is an example of a predicate in Predicate Logic?

  1. \(x \ge 0\)
  2. \(x + y = z\)
  3. \(\sin x = 0\)
  4. \(x \in \mathbb{R}\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The expression (x \ge 0) is an example of a predicate in Predicate Logic because it is a statement that can be either true or false depending on the value of (x).