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
Which of the following sets is countable?
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The set of all finite subsets of the natural numbers
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The set of all infinite subsets of the natural numbers
-
The set of all subsets of the natural numbers
-
The set of all functions from the natural numbers to the natural numbers
A
Correct answer
Explanation
The set of all finite subsets of the natural numbers is countable because it can be put into a one-to-one correspondence with the set of natural numbers.
Which of the following sets is uncountable?
-
The set of all finite subsets of the natural numbers
-
The set of all infinite subsets of the natural numbers
-
The set of all subsets of the natural numbers
-
The set of all functions from the natural numbers to the natural numbers
D
Correct answer
Explanation
The set of all functions from the natural numbers to the natural numbers is uncountable because it cannot be put into a one-to-one correspondence with the set of natural numbers.
Which of the following sets is countable?
-
The set of all finite subsets of the natural numbers
-
The set of all infinite subsets of the natural numbers
-
The set of all subsets of the natural numbers
-
The set of all functions from the natural numbers to the natural numbers
A
Correct answer
Explanation
The set of all finite subsets of the natural numbers is countable because it can be put into a one-to-one correspondence with the set of natural numbers.
Which of the following sets is uncountable?
-
The set of all finite subsets of the natural numbers
-
The set of all infinite subsets of the natural numbers
-
The set of all subsets of the natural numbers
-
The set of all functions from the natural numbers to the natural numbers
B
Correct answer
Explanation
The set of all infinite subsets of the natural numbers is uncountable because it cannot be put into a one-to-one correspondence with the set of natural numbers.
Which of the following sets is countable?
-
The set of all finite subsets of the natural numbers
-
The set of all infinite subsets of the natural numbers
-
The set of all subsets of the natural numbers
-
The set of all functions from the natural numbers to the natural numbers
A
Correct answer
Explanation
The set of all finite subsets of the natural numbers is countable because it can be put into a one-to-one correspondence with the set of natural numbers.
Which of the following sets is uncountable?
-
The set of all finite subsets of the natural numbers
-
The set of all infinite subsets of the natural numbers
-
The set of all subsets of the natural numbers
-
The set of all functions from the natural numbers to the natural numbers
D
Correct answer
Explanation
The set of all functions from the natural numbers to the natural numbers is uncountable because it cannot be put into a one-to-one correspondence with the set of natural numbers.
Which of the following sets is countable?
-
The set of all finite subsets of the natural numbers
-
The set of all infinite subsets of the natural numbers
-
The set of all subsets of the natural numbers
-
The set of all functions from the natural numbers to the natural numbers
A
Correct answer
Explanation
The set of all finite subsets of the natural numbers is countable because it can be put into a one-to-one correspondence with the set of natural numbers.
Which of the following sets is uncountable?
-
The set of all finite subsets of the natural numbers
-
The set of all infinite subsets of the natural numbers
-
The set of all subsets of the natural numbers
-
The set of all functions from the natural numbers to the natural numbers
B
Correct answer
Explanation
The set of all infinite subsets of the natural numbers is uncountable because it cannot be put into a one-to-one correspondence with the set of natural numbers.
Which of the following sets is countable?
-
The set of all finite subsets of the natural numbers
-
The set of all infinite subsets of the natural numbers
-
The set of all subsets of the natural numbers
-
The set of all functions from the natural numbers to the natural numbers
A
Correct answer
Explanation
The set of all finite subsets of the natural numbers is countable because it can be put into a one-to-one correspondence with the set of natural numbers.
Which of the following sets is uncountable?
-
The set of all finite subsets of the natural numbers
-
The set of all infinite subsets of the natural numbers
-
The set of all subsets of the natural numbers
-
The set of all functions from the natural numbers to the natural numbers
D
Correct answer
Explanation
The set of all functions from the natural numbers to the natural numbers is uncountable because it cannot be put into a one-to-one correspondence with the set of natural numbers.
What is the symbol for the universal set?
A
Correct answer
Explanation
The symbol U is used to represent the universal set.
What is the symbol for the intersection of two sets?
A
Correct answer
Explanation
The symbol ∩ is used to represent the intersection of two sets.
What is the symbol for the union of two sets?
A
Correct answer
Explanation
The symbol ∪ is used to represent the union of two sets.
What is the symbol for the complement of a set?
A
Correct answer
Explanation
The symbol ∁ is used to represent the complement of a set.
What is the symbol for the power set of a set?
A
Correct answer
Explanation
The symbol ℘ is used to represent the power set of a set.