Home › Quizzes › Cardinality and Set Operations: A Journey into the World of Infinite Sets

Cardinality and Set Operations: A Journey into the World of Infinite Sets

Welcome to the quiz on Cardinality and Set Operations, where we'll explore the fascinating world of infinite sets and their properties. Get ready to test your understanding of set theory concepts and operations.

15 Questions Published
Play Quiz Practise this topic out loud

Questions

Question 1 Multiple Choice (Single Answer)

Which of the following sets has a cardinality of (\aleph_0)?

  1. The set of all natural numbers \(\mathbb{N}\)
  2. The set of all real numbers \(\mathbb{R}\)
  3. The set of all even integers \(2\mathbb{Z}\)
  4. The set of all prime numbers \(\mathbb{P}\)
Question 2 Multiple Choice (Single Answer)

Which of the following sets is uncountable?

  1. The set of all rational numbers \(\mathbb{Q}\)
  2. The set of all algebraic numbers \(\mathbb{A}\)
  3. The set of all transcendental numbers \(\mathbb{T}\)
  4. The set of all constructible numbers \(\mathbb{C}\)
Question 3 Multiple Choice (Single Answer)

What is the cardinality of the power set of a set with (n) elements?

  1. \(n\)
  2. \(2^n\)
  3. \(n^2\)
  4. \(n!\)
Question 4 Multiple Choice (Single Answer)

Which of the following operations is not associative on sets?

  1. Union \(\cup\)
  2. Intersection \(\cap\)
  3. Symmetric difference \(\Delta\)
  4. Complement \(\)\)
Question 5 Multiple Choice (Single Answer)

What is the distributive law of set operations?

  1. \(A\cap(B\cup C) = (A\cap B)\cup(A\cap C)\)
  2. \(A\cup(B\cap C) = (A\cup B)\cap(A\cup C)\)
  3. \(A\Delta(B\cup C) = (A\Delta B)\cup(A\Delta C)\)
  4. \(A\Delta(B\cap C) = (A\Delta B)\cap(A\Delta C)\)
Question 6 Multiple Choice (Single Answer)

Which of the following is an example of a bijection between two sets?

  1. The function \(f(x) = x^2\) from \(\mathbb{R}\) to \(\mathbb{R}\)
  2. The function \(f(x) = \sin(x)\) from \(\mathbb{R}\) to \([0, 1]\)
  3. The function \(f(x) = \lfloor x \rfloor\) from \(\mathbb{R}\) to \(\mathbb{Z}\)
  4. The function \(f(x) = \lceil x \rceil\) from \(\mathbb{R}\) to \(\mathbb{Z}\)
Question 7 Multiple Choice (Single Answer)

What is the cardinality of the set of all subsets of a set with (n) elements?

  1. \(n\)
  2. \(2^n\)
  3. \(n^2\)
  4. \(n!\)
Question 8 Multiple Choice (Single Answer)

Which of the following sets is not closed under the operation of union?

  1. The set of all natural numbers \(\mathbb{N}\)
  2. The set of all even integers \(2\mathbb{Z}\)
  3. The set of all rational numbers \(\mathbb{Q}\)
  4. The set of all real numbers \(\mathbb{R}\)
Question 9 Multiple Choice (Single Answer)

What is the cardinality of the set of all functions from a set with (m) elements to a set with (n) elements?

  1. \(m\)
  2. \(n\)
  3. \(m^n\)
  4. \(n^m\)
Question 10 Multiple Choice (Single Answer)

Which of the following is an example of a one-to-one function?

  1. The function \(f(x) = x^2\) from \(\mathbb{R}\) to \(\mathbb{R}\)
  2. The function \(f(x) = \sin(x)\) from \(\mathbb{R}\) to \([0, 1]\)
  3. The function \(f(x) = \lfloor x \rfloor\) from \(\mathbb{R}\) to \(\mathbb{Z}\)
  4. The function \(f(x) = \lceil x \rceil\) from \(\mathbb{R}\) to \(\mathbb{Z}\)
Question 11 Multiple Choice (Single Answer)

What is the cardinality of the set of all real numbers between 0 and 1?

  1. \(\aleph_0\)
  2. \(\aleph_1\)
  3. \(\continuum\)
  4. \(\infty\)
Question 12 Multiple Choice (Single Answer)

Which of the following is an example of an onto function?

  1. The function \(f(x) = x^2\) from \(\mathbb{R}\) to \(\mathbb{R}\)
  2. The function \(f(x) = \sin(x)\) from \(\mathbb{R}\) to \([0, 1]\)
  3. The function \(f(x) = \lfloor x \rfloor\) from \(\mathbb{R}\) to \(\mathbb{Z}\)
  4. The function \(f(x) = \lceil x \rceil\) from \(\mathbb{R}\) to \(\mathbb{Z}\)
Question 13 Multiple Choice (Single Answer)

What is the cardinality of the set of all subsets of a set with (\aleph_0) elements?

  1. \(\aleph_0\)
  2. \(\aleph_1\)
  3. \(\continuum\)
  4. \(\infty\)
Question 14 Multiple Choice (Single Answer)

Which of the following is an example of a bijective function?

  1. The function \(f(x) = x^2\) from \(\mathbb{R}\) to \(\mathbb{R}\)
  2. The function \(f(x) = \sin(x)\) from \(\mathbb{R}\) to \([0, 1]\)
  3. The function \(f(x) = \lfloor x \rfloor\) from \(\mathbb{R}\) to \(\mathbb{Z}\)
  4. The function \(f(x) = \lceil x \rceil\) from \(\mathbb{R}\) to \(\mathbb{Z}\)
Question 15 Multiple Choice (Single Answer)

What is the cardinality of the set of all functions from a set with (\aleph_0) elements to a set with (\aleph_1) elements?

  1. \(\aleph_0\)
  2. \(\aleph_1\)
  3. \(\continuum\)
  4. \(\infty\)
← Back to Quizzes