Mathematics

Set Theory and Relations

368 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

The intersection of two sets A and B is denoted by which symbol?

  1. ∪

  2. ∩

  3. ∅

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

The intersection of two sets A and B, denoted by A ∩ B, is the set of elements that are common to both A and B.

Multiple choice

The union of two sets A and B is denoted by which symbol?

  1. ∪

  2. ∩

  3. ∅

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

The union of two sets A and B, denoted by A ∪ B, is the set of elements that are in either A or B or both.

Multiple choice

The complement of a set A with respect to a universal set U is denoted by which symbol?

  1. A'

  2. Aᶜ

  3. U - A

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

The complement of a set A with respect to a universal set U, denoted by Aᶜ, is the set of elements in U that are not in A.

Multiple choice

The power set of a set A is denoted by which symbol?

  1. P(A)

  2. A'

  3. Aᶜ

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

The power set of a set A, denoted by P(A), is the set of all subsets of A.

Multiple choice

The Cartesian product of two sets A and B is denoted by which symbol?

  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 Cartesian product of two sets A and B, denoted by A × B, is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B.

Multiple choice

The relation between two sets A and B is denoted by which symbol?

  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 relation between two sets A and B, denoted by A → B, means that every element of A is also an element of B.

Multiple choice

What is the Hausdorff dimension of the Cantor set?

  1. 0

  2. 1

  3. 2

  4. 3
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

The Hausdorff dimension of a set is a measure of its fractal dimension. The Cantor set is a fractal set that is constructed by repeatedly removing the middle third of each interval in a sequence of nested intervals. The Hausdorff dimension of the Cantor set is log(3)/log(2), which is approximately 0.6309.

Multiple choice

What is the fundamental building block of set theory?

  1. Element

  2. Set

  3. Axiom

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

An element is a member of a set, and sets are defined by the elements they contain.

Multiple choice

Which mathematical principle states that for any two sets A and B, the union of A and B is the set of all elements that are in either A or B?

  1. Union Principle

  2. Intersection Principle

  3. Complement Principle

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

The union principle is a fundamental principle of set theory that defines the union of two sets.

Multiple choice

What is the mathematical principle that states that for any two sets A and B, the intersection of A and B is the set of all elements that are in both A and B?

  1. Union Principle

  2. Intersection Principle

  3. Complement Principle

  4. Distributive Principle
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The intersection principle is a fundamental principle of set theory that defines the intersection of two sets.

Multiple choice

What is the mathematical principle that states that for any three sets A, B, and C, the union of A, B, and C is the set of all elements that are in at least one of the three sets?

  1. Union Principle

  2. Intersection Principle

  3. Complement Principle

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

The union principle is a fundamental principle of set theory that defines the union of three sets.

Multiple choice

What is the mathematical principle that states that for any two sets A and B, the complement of A with respect to B is the set of all elements that are in B but not in A?

  1. Union Principle

  2. Intersection Principle

  3. Complement Principle

  4. Distributive Principle
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The complement principle is a fundamental principle of set theory that defines the complement of a set with respect to another set.

Multiple choice

What is the mathematical principle that states that for any three sets A, B, and C, the intersection of A, B, and C is the set of all elements that are in all three sets?

  1. Union Principle

  2. Intersection Principle

  3. Complement Principle

  4. Distributive Principle
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The intersection principle is a fundamental principle of set theory that defines the intersection of three sets.

Multiple choice

In set theory, the power set of a set A is defined as:

  1. The set of all subsets of A

  2. The set of all elements of A

  3. The set of all ordered pairs of elements from A

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

The power set of a set A is the set of all subsets of A, including the empty set and the set A itself.

Multiple choice

In set theory, the Cartesian product of two sets A and B is defined as:

  1. The set of all ordered pairs (a, b) where a is in A and b is in B

  2. The set of all unordered pairs (a, b) where a is in A and b is in B

  3. The set of all subsets of A and B

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

The Cartesian product of two sets A and B is the set of all ordered pairs (a, b) where a is in A and b is in B.