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Discrete Mathematics | Types of Sets MCQs

Discrete Mathematics | Types of Sets MCQs: This section contains multiple-choice questions and answers on Types of Sets in Discrete Mathematics.
Submitted by Anushree Goswami, on July 10, 2022

1. ____, universal, proper, singleton, and power set are a few of the many types of sets.

  1. Finite
  2. Infinite
  3. Subset
  4. All of the above

Answer: D) All of the above

Explanation:

Finite, infinite, subset, universal, proper, singleton, and power set are a few of the many types of sets.


2. Whenever n is a non-negative integer then a set is said to be finite if it contains only ____ distinct elements.

  1. n
  2. n+1
  3. n-1
  4. n^2

Answer: A) n

Explanation:

Whenever n is a non-negative integer then a set is said to be finite if it contains only n distinct elements.


3. ____ or #A are used to denote the cardinality of sets.

  1. Card (A)
  2. Card |A|
  3. n(A)
  4. All of the above

Answer: D) All of the above

Explanation:

Cards (A), #A, cards (A), or n (A) are used to denote the cardinality of sets.


4. Whenever there is a one-to-one correspondence between an element in the set and an element in some other set n, where n is a natural number and n is the cardinality of the set, the set is called a ____ set.

  1. Finite
  2. Infinite
  3. Subset
  4. Cardinality

Answer: A) Finite

Explanation:

Whenever there is a one-to-one correspondence between an element in the set and an element in some other set n, where n is a natural number and n is the cardinality of the set, the set is called a finite set.


5. An ____ set is a finite set.

  1. Enumerable
  2. Innumberable
  3. Both A and B
  4. None of the above

Answer: A) Enumerable

Explanation:

An enumerable set is a finite set.


6. An ____ set is one that has no end.

  1. Non-finite
  2. Finite
  3. Infinite
  4. None

Answer: C) Infinite

An infinite set is one that has no end.


7. The ____ is n.

  1. Cardinality of sets
  2. Cardinal number of sets
  3. Both A and B
  4. None of the above

Answer: C) Both A and B

Explanation:

The cardinality of sets or a cardinal number of sets is n.


8. _____ is when the elements in set and the elements in N correspond one-to-one.

  1. Countable finite
  2. Uncountable finite
  3. Uncountable finite
  4. Countable infinite

Answer: A) Countable finite

Explanation:

Countable infinite is when the elements in set and the elements in N correspond one-to-one.


9. ____ is another name for a countably infinite set.

  1. Enumerable
  2. Denumerable
  3. Non-numerable
  4. Innumberable

Answer: B) Denumerable

Explanation:

Denumerable is another name for a countably infinite set.


10. In mathematics, countable sets are defined as ____.

  1. Finite
  2. Denumerable
  3. Both A and B
  4. None of the above

Answer: C) Both A and B

Explanation:

In mathematics, countable sets are defined as finite or denumerable.


11. ____ sets are sets that cannot be counted.

  1. Countable
  2. Uncountable
  3. Decountable
  4. None

Answer: A) Countable

Explanation:

Uncountable sets are sets that cannot be counted.


12. A non-negative even integer set is ____.

  1. Countable Finite
  2. Countable Infinite
  3. Uncountable Finite
  4. Uncountable Infinite

Answer: A) Countable Finite

Explanation:

A non-negative even integer set is countable infinite.


13. Infinite sets that can't be counted are called _____.

  1. Uncountable Infinite sets
  2. Non-denumerable sets
  3. Uncountable sets
  4. All of the above

Answer: D) All of the above

Explanation:

Infinite sets that can't be counted are called uncountable infinite sets, non-denumerable sets, or just Uncountable sets.


14. A is called a subset of B, if ____ element of A is also an element of B.

  1. Few
  2. None
  3. Every
  4. Little

Answer: C) Every

Explanation:

A is called a subset of B, if every element of A is also an element of B.


15. If every element of A is also an element of B, it is denoted by -

  1. A ⊆ B
  2. A U B
  3. A - B
  4. A + B

Answer: A) A ⊆ B

Explanation:

If every element of A is also an element of B, it is denoted by A ⊆ B.


16. If every element of A is also an element of B, then -

  1. A is called Superset of B
  2. B is called Superset of A
  3. A and B are Superset
  4. B is called Subset of A

Answer: B) B is called Superset of A

Explanation:

If every element of A is also an element of B, then B is called Superset of A.


17. Which of the following is/are a property (ies) of a subset?

  1. Sets are subsets of one another.
  2. Every set contains a Null Set, i.e.∅.
  3. The subset of A will be C if it is a subset of B and B is a subset of C.
  4. All of the above

Answer: D) All of the above

Explanation:

Following are the properties of a subset -

  1. Sets are subsets of one another.
  2. Every set contains a Null Set, i.e.∅.
  3. The subset of A will be C if it is a subset of B and B is a subset of C.

18. Which of the following is a property of a subset?

  1. If there are n elements in a finite set, there are 2^n subsets
  2. If there are n elements in a finite set, there are n^2 subsets
  3. If there are n elements in an infinite set, there are 2^n subsets
  4. If there are n elements in an infinite set, there are n^2 subsets

Answer: A) If there are n elements in a finite set, there are 2^n subsets

Explanation:

If there are n elements in a finite set, there are 2^n subsets.


19. If A⊂B and B⊂ C ⟹ ____

  1. A ⊂ C
  2. C ⊂ A
  3. A U C
  4. A + C

Answer: A) A ⊂ C

Explanation:

If A⊂B and B⊂ C ⟹ A ⊂ C


20. Whenever A is a subset of B, and A ≠ B, then A is called a ___ subset of B.

  1. Proper
  2. Improper
  3. Finite
  4. Infinite

Answer: A) Proper

Explanation:

Whenever A is a subset of B, and A ≠ B, then A is called a proper subset of B.


21. B ____ of A if A is a proper subset of B.

  1. Is not a subset
  2. Is a subset
  3. Is not a superset
  4. None

Answer: A) Is not a subset

Explanation:

B is not a subset of A if A is a proper subset of B.


22. Every set has a null ____ as a proper subset.

  1. =
  2. *
  3. U

Answer: A) ∅

Explanation:

Every set has a null ∅ as a proper subset.


23. A is said to be an ____ subset of B if A is a subset of B and A = B.

  1. Proper
  2. Improper
  3. Enumerable
  4. Denumerable

Answer: B) Improper

Explanation:

A is said to be an improper subset of B if A is a subset of B and A = B.


24. Sets are ____ subsets of themselves.

  1. Proper
  2. Improper
  3. Finite
  4. Infinite

Answer: B) Improper

Explanation:

Sets are improper subsets of themselves.


25. An investigation set U is called _____ Set if it contains all the sets under investigation.

  1. Universal
  2. Null
  3. Empty
  4. Singelton

Answer: A) Universal

Explanation:

An investigation set U is called Universal Set if it contains all the sets under investigation.


26. ____ sets, do not contain any elements.

  1. Null
  2. Void
  3. Empty
  4. All of the above

Answer: D) All of the above

Explanation:

Null sets, or void sets, do not contain any elements.


27. Singleton set contains ___ element.

  1. Null
  2. One
  3. Multiple
  4. Infinite

Answer: B) One

Explanation:

Singleton set contains one element.


28. When both sets A and B have the same elements, they are ____ and written as A = B.

  1. Equal
  2. Non-equal
  3. Finite
  4. Infinite

Answer: B) Non-equal

Explanation:

When both sets A and B have the same elements, they are equal and written as A = B.


29. Equivalent sets are those whose ____ are equal.

  1. Elements
  2. Sets
  3. Cardinalities
  4. None

Answer: C) Cardinalities

Explanation:

Equivalent sets are those whose cardinalities are equal.


30. Any element of A cannot be found in B and any element of B cannot be found in A if two sets A and B are ____.

  1. Joint
  2. Disjoint
  3. Null
  4. Singleton

Answer: B) Disjoint

Explanation:

An element of A cannot be found in B and an element of B cannot be found in A if two sets A and B are disjoint.


31. Set of all ____ of A are called its power.

  1. Subsets
  2. Sets
  3. Supersets
  4. None

Answer: A) Subsets

Explanation:

Set of all subsets of A are called its power.


32. Subdividing S into ____ subsets is known as partitioning S.

  1. Nonoverlapping
  2. Nonempty
  3. Both A and B
  4. None of the above

Answer: C) Both A and B

Explanation:

Subdividing S into nonoverlapping, nonempty subsets is known as partitioning S.


33. Cells are the ____ in a partition.

  1. Subsets
  2. Sets
  3. Supersets
  4. None

Answer: A) Subsets

Explanation:

Cells are the subsets in a partition.


34. When set is represented in pictorial format, it is known as -

  1. Pictorial Diagram
  2. Vven Diagram
  3. Veen Diagram
  4. Venn Diagram

Answer: D) Venn Diagram

Explanation:

When set is represented in pictorial format, it is known as Venn Diagram.





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