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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.**

- Finite
- Infinite
- Subset
- 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.**

- n
- n+1
- n-1
- 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.**

- Card (A)
- Card |A|
- n(A)
- 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.**

- Finite
- Infinite
- Subset
- 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.**

- Enumerable
- Innumberable
- Both A and B
- None of the above

**Answer:** A) Enumerable

**Explanation:**

An enumerable set is a finite set.

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

- Non-finite
- Finite
- Infinite
- None

**Answer:** C) Infinite

An infinite set is one that has no end.

**7. The ____ is n.**

- Cardinality of sets
- Cardinal number of sets
- Both A and B
- 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.**

- Countable finite
- Uncountable finite
- Uncountable finite
- 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.**

- Enumerable
- Denumerable
- Non-numerable
- Innumberable

**Answer:** B) Denumerable

**Explanation:**

Denumerable is another name for a countably infinite set.

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

- Finite
- Denumerable
- Both A and B
- 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.**

- Countable
- Uncountable
- Decountable
- None

**Answer:** A) Countable

**Explanation:**

Uncountable sets are sets that cannot be counted.

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

- Countable Finite
- Countable Infinite
- Uncountable Finite
- 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 _____.**

- Uncountable Infinite sets
- Non-denumerable sets
- Uncountable sets
- 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.**

- Few
- None
- Every
- 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 -**

- A ⊆ B
- A U B
- A - B
- 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 -**

- A is called Superset of B
- B is called Superset of A
- A and B are Superset
- 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?**

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

**Answer:** D) All of the above

**Explanation:**

Following are the properties of a subset -

- Sets are subsets of one another.
- Every set contains a Null Set, i.e.∅.
- 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?**

- If there are n elements in a finite set, there are 2^n subsets
- If there are n elements in a finite set, there are n^2 subsets
- If there are n elements in an infinite set, there are 2^n subsets
- 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 ⟹ ____**

- A ⊂ C
- C ⊂ A
- A U C
- 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.**

- Proper
- Improper
- Finite
- 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.**

- Is not a subset
- Is a subset
- Is not a superset
- 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.**

- ∅
- =
- *
- 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.**

- Proper
- Improper
- Enumerable
- 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.**

- Proper
- Improper
- Finite
- 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.**

- Universal
- Null
- Empty
- 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.**

- Null
- Void
- Empty
- 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.**

- Null
- One
- Multiple
- 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.**

- Equal
- Non-equal
- Finite
- 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.**

- Elements
- Sets
- Cardinalities
- 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 ____.**

- Joint
- Disjoint
- Null
- 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.**

- Subsets
- Sets
- Supersets
- 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.**

- Nonoverlapping
- Nonempty
- Both A and B
- 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.**

- Subsets
- Sets
- Supersets
- None

**Answer:** A) Subsets

**Explanation:**

Cells are the subsets in a partition.

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

- Pictorial Diagram
- Vven Diagram
- Veen Diagram
- Venn Diagram

**Answer:** D) Venn Diagram

**Explanation:**

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

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