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

What is the symbol for the union 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 union of two sets.

Multiple choice

What is the symbol for the complement of a set?

  1. ∁

  2. ∩

  3. ∪

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

The symbol ∁ is used to represent the complement of a set.

Multiple choice

What is the symbol for the power set of a set?

  1. ℘

  2. ∩

  3. ∪

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

The symbol ℘ is used to represent the power set of a set.

Multiple choice

What is the symbol for the Cartesian product 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 Cartesian product of two sets.

Multiple choice

Given the sets A = {1, 3, 5} and B = {2, 4, 6}, what is the union of A and B?

  1. {1, 2, 3, 4, 5, 6}

  2. {1, 3, 5, 2, 4, 6}

  3. {1, 2, 3, 4, 5}

  4. {1, 3, 5, 6}
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The union of two sets A and B, denoted as A ∪ B, is the set of all elements that are in either A or B. Therefore, the union of A = {1, 3, 5} and B = {2, 4, 6} is {1, 2, 3, 4, 5, 6}.

Multiple choice

What is the intersection of the sets A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}?

  1. {1, 2}

  2. {3, 4, 5}

  3. {1, 2, 3, 4, 5, 6, 7}

  4. {6, 7}
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The intersection of two sets A and B, denoted as A ∩ B, is the set of all elements that are in both A and B. Therefore, the intersection of A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7} is {3, 4, 5}.

Multiple choice

What is the cardinality of the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}?

  1. 5

  2. 10

  3. 15

  4. 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The cardinality of a set is the number of elements in the set. The set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} contains 10 elements. Therefore, the cardinality of A is 10.

Multiple choice

Which of the following sets is a subset of the set B = {1, 3, 5, 7, 9}?

  1. {1, 2, 3, 4, 5}

  2. {1, 3, 5}

  3. {2, 4, 6, 8}

  4. {0, 2, 4, 6, 8}
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A subset of a set B is a set that contains only elements that are also in B. The set {1, 3, 5} is a subset of B because every element of {1, 3, 5} is also an element of B. The other sets are not subsets of B because they contain elements that are not in B.

Multiple choice

What is the complement of the set A = {1, 3, 5} in the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}?

  1. {2, 4, 6, 8, 10}

  2. {2, 4, 6, 8}

  3. {2, 3, 4, 6, 8, 9, 10}

  4. {2, 4, 6, 8, 9}
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The complement of a set A in a universal set U is the set of all elements in U that are not in A. The complement of A = {1, 3, 5} in U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is {2, 4, 6, 8, 10}.

Multiple choice

Which of the following is an example of a power set?

  1. {1, 2, 3}

  2. {1, {2, 3}, 4}

  3. {1, 2, {3, 4}}

  4. {{1, 2}, {3, 4}, {5, 6}}
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The power set of a set A is the set of all subsets of A. The set {{1, 2}, {3, 4}, {5, 6}} is the power set of the set {1, 2, 3, 4, 5, 6} because it contains all possible subsets of {1, 2, 3, 4, 5, 6}.