Home › Quizzes › Axiomatic Set Theory

Axiomatic Set Theory

This quiz is designed to test your understanding of the fundamental concepts and axioms of Axiomatic Set Theory, a branch of mathematics that studies the properties of sets and their relationships.

14 Questions Published
Play Quiz Practise this topic out loud

Questions

Question 1 Multiple Choice (Single Answer)

Which of the following is an axiom of Zermelo-Fraenkel Set Theory?

  1. The Axiom of Extensionality
  2. The Axiom of Pairing
  3. The Axiom of Union
  4. The Axiom of Choice
Question 2 Multiple Choice (Single Answer)

What is the Axiom of Extensionality?

  1. Two sets are equal if and only if they have the same elements.
  2. A set can be defined by its properties.
  3. The union of two sets is the set of all elements that are in either set.
  4. Every set has a unique complement.
Question 3 Multiple Choice (Single Answer)

What is the Axiom of Pairing?

  1. Two sets can be paired to form a new set.
  2. A set can be defined by its properties.
  3. The union of two sets is the set of all elements that are in either set.
  4. Every set has a unique complement.
Question 4 Multiple Choice (Single Answer)

What is the Axiom of Union?

  1. Two sets can be paired to form a new set.
  2. A set can be defined by its properties.
  3. The union of two sets is the set of all elements that are in either set.
  4. Every set has a unique complement.
Question 5 Multiple Choice (Single Answer)

What is the Axiom of Choice?

  1. Two sets can be paired to form a new set.
  2. A set can be defined by its properties.
  3. The union of two sets is the set of all elements that are in either set.
  4. Given a collection of non-empty sets, there exists a function that selects an element from each set.
Question 6 Multiple Choice (Single Answer)

What is Russell's Paradox?

  1. A set that contains itself as an element.
  2. A set that is empty.
  3. A set that is infinite.
  4. A set that is well-ordered.
Question 7 Multiple Choice (Single Answer)

What is the Zermelo-Fraenkel set theory?

  1. A set of axioms used to define the concept of a set.
  2. A set of axioms used to define the concept of a function.
  3. A set of axioms used to define the concept of a relation.
  4. A set of axioms used to define the concept of a number.
Question 8 Multiple Choice (Single Answer)

Which of the following is not an axiom of Zermelo-Fraenkel set theory?

  1. The Axiom of Extensionality
  2. The Axiom of Pairing
  3. The Axiom of Union
  4. The Axiom of Infinity
Question 9 Multiple Choice (Single Answer)

What is the Axiom of Regularity?

  1. Every non-empty set contains an element that is disjoint from the set.
  2. Every non-empty set contains an element that is a subset of the set.
  3. Every non-empty set contains an element that is a proper subset of the set.
  4. Every non-empty set contains an element that is a member of the set.
Question 10 Multiple Choice (Single Answer)

What is the Axiom of Replacement?

  1. If a set A is a subset of a set B, then there exists a set C that is isomorphic to A and a function f from B to C such that f(A) = C.
  2. If a set A is a subset of a set B, then there exists a set C that is isomorphic to A and a function f from C to B such that f(A) = C.
  3. If a set A is a subset of a set B, then there exists a set C that is isomorphic to A and a function f from A to C such that f(A) = C.
  4. If a set A is a subset of a set B, then there exists a set C that is isomorphic to A and a function f from B to A such that f(A) = C.
Question 11 Multiple Choice (Single Answer)

What is the Power Set Axiom?

  1. For any set A, there exists a set B that contains all the subsets of A.
  2. For any set A, there exists a set B that contains all the elements of A.
  3. For any set A, there exists a set B that is isomorphic to A.
  4. For any set A, there exists a set B that is a proper subset of A.
Question 12 Multiple Choice (Single Answer)

What is the Axiom of Choice?

  1. Given a collection of non-empty sets, there exists a function that selects an element from each set.
  2. Given a collection of non-empty sets, there exists a set that contains all the elements of all the sets in the collection.
  3. Given a collection of non-empty sets, there exists a set that is isomorphic to the union of all the sets in the collection.
  4. Given a collection of non-empty sets, there exists a set that is a proper subset of the union of all the sets in the collection.
Question 13 Multiple Choice (Single Answer)

What is the Axiom of Infinity?

  1. There exists a set that contains infinitely many elements.
  2. There exists a set that is isomorphic to the set of natural numbers.
  3. There exists a set that is a proper subset of the set of natural numbers.
  4. There exists a set that is a superset of the set of natural numbers.
Question 14 Multiple Choice (Single Answer)

What is the Axiom of Foundation?

  1. Every non-empty set contains a minimal element.
  2. Every non-empty set contains a maximal element.
  3. Every non-empty set contains an element that is disjoint from the set.
  4. Every non-empty set contains an element that is a member of the set.
← Back to Quizzes