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

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

  1. n

  2. 2^n

  3. n!

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

The cardinality of the power set of a set with n elements is 2^n.

Multiple choice

If A is a set with n elements, how many subsets of A have an even number of elements?

  1. 2^(n-1)

  2. 2^n

  3. n choose (n/2)

  4. n permute (n/2)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The number of subsets of a set with n elements that have an even number of elements is 2^(n-1).

Multiple choice

Which of the following is a subset of the set {1, 2, 3, 4, 5}?

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

  2. {1, 3, 5}

  3. {2, 4}

  4. {6, 7, 8}
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A subset is a set that is contained within another set. {1, 3, 5} is a subset of {1, 2, 3, 4, 5} because every element of {1, 3, 5} is also an element of {1, 2, 3, 4, 5}.

Multiple choice

If A and B are two sets, which of the following is always true?

  1. P(A ∪ B) = P(A) ∪ P(B)

  2. P(A ∩ B) = P(A) ∩ P(B)

  3. P(A - B) = P(A) - P(B)

  4. P(A × B) = P(A) × P(B)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The power set of the union of two sets is equal to the union of the power sets of the two sets.

Multiple choice

What is the cardinality of the power set of a set with 3 elements?

  1. 3

  2. 6

  3. 8

  4. 9
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The cardinality of the power set of a set with 3 elements is 8.

Multiple choice

If A is a set with n elements, how many subsets of A have an odd number of elements?

  1. 2^(n-1)

  2. 2^n

  3. n choose (n/2)

  4. n permute (n/2)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The number of subsets of a set with n elements that have an odd number of elements is 2^(n-1).

Multiple choice

Which of the following is a proper subset of the set {1, 2, 3, 4, 5}?

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

  2. {1, 2, 3}

  3. {1, 3, 5}

  4. {2, 4, 5}
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A proper subset is a subset that is not equal to the original set. {1, 3, 5} is a proper subset of {1, 2, 3, 4, 5} because it is a subset and it is not equal to the original set.

Multiple choice

If A and B are two sets, which of the following is always true?

  1. P(A ∩ B) = P(A) ∩ P(B)

  2. P(A ∪ B) = P(A) ∪ P(B)

  3. P(A - B) = P(A) - P(B)

  4. P(A × B) = P(A) × P(B)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The power set of the intersection of two sets is equal to the intersection of the power sets of the two sets.

Multiple choice

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

  1. n

  2. 2^n

  3. n!

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

The cardinality of the power set of a set with n elements is 2^n.

Multiple choice

Which of the following is a set?

  1. A collection of distinct objects

  2. A list of numbers

  3. A mathematical expression

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

A set is a well-defined collection of distinct objects, which can be any type of entity, such as numbers, letters, shapes, or even other sets.

Multiple choice

What is the symbol used to represent the union of two sets?

  1. ∩

  2. ∪

  3. −

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

The union of two sets, denoted by ∪, is the set of all elements that are in either of the two sets.

Multiple choice

What is the symbol used to represent the intersection of two sets?

  1. ∩

  2. ∪

  3. −

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

The intersection of two sets, denoted by ∩, is the set of all elements that are in both of the two sets.

Multiple choice

What is the symbol used to represent the complement of a set?

  1. ∩

  2. ∪

  3. −

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

The complement of a set, denoted by −, is the set of all elements that are not in the given set.

Multiple choice

What is the power set of a set?

  1. The set of all subsets of the given set

  2. The set of all elements of the given set

  3. The set of all complements of the given set

  4. The set of all unions of the given set
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

Multiple choice

What is the Cartesian product of two sets?

  1. The set of all ordered pairs of elements from the two sets

  2. The set of all unordered pairs of elements from the two sets

  3. The set of all elements that are in both of the two sets

  4. The set of all elements that are not in either of the two sets
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Cartesian product of two sets is the set of all ordered pairs of elements, where the first element is from the first set and the second element is from the second set.