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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.