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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Explanation:

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