Mathematics

Set Theory and Relations

355 Questions

Set theory involves the study of collections of objects and includes operations like union, intersection, and finding complements. Questions cover power sets, Cartesian products, and properties of empty sets. This foundational mathematical topic frequently appears in various competitive exams and university entrance tests.

set operationspower setscartesian productsset complementsproperties of empty setsset partitions

Set Theory and Relations Questions

Multiple choice

Which of the following sets has the same cardinality as the set of natural numbers?

  1. The set of all integers

  2. The set of all rational numbers

  3. The set of all real numbers

  4. The set of all complex numbers
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The set of all integers has the same cardinality as the set of natural numbers because it can be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

Which of the following sets has a larger cardinality than the set of natural numbers?

  1. The set of all rational numbers

  2. The set of all real numbers

  3. The set of all complex numbers

  4. The set of all functions from the natural numbers to the natural numbers
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The set of all real numbers has a larger cardinality than the set of natural numbers because it cannot be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

Which of the following sets is uncountable?

  1. The set of all finite subsets of the natural numbers

  2. The set of all infinite subsets of the natural numbers

  3. The set of all subsets of the natural numbers

  4. The set of all functions from the natural numbers to the natural numbers
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The set of all infinite subsets of the natural numbers is uncountable because it cannot be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

Which of the following sets is countable?

  1. The set of all finite subsets of the natural numbers

  2. The set of all infinite subsets of the natural numbers

  3. The set of all subsets of the natural numbers

  4. The set of all functions from the natural numbers to the natural numbers
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The set of all finite subsets of the natural numbers is countable because it can be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

Which of the following sets is uncountable?

  1. The set of all finite subsets of the natural numbers

  2. The set of all infinite subsets of the natural numbers

  3. The set of all subsets of the natural numbers

  4. The set of all functions from the natural numbers to the natural numbers
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The set of all functions from the natural numbers to the natural numbers is uncountable because it cannot be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

Which of the following sets is countable?

  1. The set of all finite subsets of the natural numbers

  2. The set of all infinite subsets of the natural numbers

  3. The set of all subsets of the natural numbers

  4. The set of all functions from the natural numbers to the natural numbers
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The set of all finite subsets of the natural numbers is countable because it can be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

Which of the following sets is uncountable?

  1. The set of all finite subsets of the natural numbers

  2. The set of all infinite subsets of the natural numbers

  3. The set of all subsets of the natural numbers

  4. The set of all functions from the natural numbers to the natural numbers
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The set of all infinite subsets of the natural numbers is uncountable because it cannot be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

Which of the following sets is countable?

  1. The set of all finite subsets of the natural numbers

  2. The set of all infinite subsets of the natural numbers

  3. The set of all subsets of the natural numbers

  4. The set of all functions from the natural numbers to the natural numbers
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The set of all finite subsets of the natural numbers is countable because it can be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

Which of the following sets is uncountable?

  1. The set of all finite subsets of the natural numbers

  2. The set of all infinite subsets of the natural numbers

  3. The set of all subsets of the natural numbers

  4. The set of all functions from the natural numbers to the natural numbers
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The set of all functions from the natural numbers to the natural numbers is uncountable because it cannot be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

Which of the following sets is countable?

  1. The set of all finite subsets of the natural numbers

  2. The set of all infinite subsets of the natural numbers

  3. The set of all subsets of the natural numbers

  4. The set of all functions from the natural numbers to the natural numbers
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The set of all finite subsets of the natural numbers is countable because it can be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

Which of the following sets is uncountable?

  1. The set of all finite subsets of the natural numbers

  2. The set of all infinite subsets of the natural numbers

  3. The set of all subsets of the natural numbers

  4. The set of all functions from the natural numbers to the natural numbers
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The set of all infinite subsets of the natural numbers is uncountable because it cannot be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

Which of the following sets is countable?

  1. The set of all finite subsets of the natural numbers

  2. The set of all infinite subsets of the natural numbers

  3. The set of all subsets of the natural numbers

  4. The set of all functions from the natural numbers to the natural numbers
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The set of all finite subsets of the natural numbers is countable because it can be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

Which of the following sets is uncountable?

  1. The set of all finite subsets of the natural numbers

  2. The set of all infinite subsets of the natural numbers

  3. The set of all subsets of the natural numbers

  4. The set of all functions from the natural numbers to the natural numbers
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The set of all functions from the natural numbers to the natural numbers is uncountable because it cannot be put into a one-to-one correspondence with the set of natural numbers.

Multiple choice

What is the symbol for the universal set?

  1. U

  2. ∅

  3. {}

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

The symbol U is used to represent the universal set.

Multiple choice

What is the symbol for the intersection of two sets?

  1. ∩

  2. ∪

  3. ∅

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

The symbol ∩ is used to represent the intersection of two sets.