Set Theory Online Test

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Set Theory

Description: This quiz covers the fundamental concepts of Set Theory, including set operations, properties, and applications.
Number of Questions: 15
Created by: Aliensbrain Bot
Tags: set theory sets operations properties applications

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What is a set?

A well-defined collection of distinct objects.
A group of objects that are related in some way.
A list of items.
A collection of numbers.

Which of the following is an example of a set?

{1, 2, 3, 4, 5}
{a, b, c, d, e}
{apple, banana, orange, pear, grape}
All of the above

What is the empty set?

A set with no elements.
A set with only one element.
A set with an infinite number of elements.
None of the above

What is the union of two sets?

The set of all elements that are in either set.
The set of all elements that are in both sets.
The set of all elements that are not in either set.
None of the above

What is the intersection of two sets?

The set of all elements that are in either set.
The set of all elements that are in both sets.
The set of all elements that are not in either set.
None of the above

What is the difference between two sets?

The set of all elements that are in the first set but not in the second set.
The set of all elements that are in the second set but not in the first set.
The set of all elements that are in both sets.
None of the above

What is the complement of a set?

The set of all elements that are not in the set.
The set of all elements that are in the set.
The set of all elements that are both in the set and not in the set.
None of the above

What is the power set of a set?

The set of all subsets of the set.
The set of all elements of the set.
The set of all complements of the set.
None of the above

What is the cardinality of a set?

The number of elements in the set.
The size of the set.
The measure of the set.
None of the above

What is the principle of inclusion-exclusion?

A method for counting the number of elements in a union of sets.
A method for counting the number of elements in an intersection of sets.
A method for counting the number of elements in a difference of sets.
None of the above

What is a partition of a set?

A collection of disjoint subsets of a set whose union is the entire set.
A collection of overlapping subsets of a set whose union is the entire set.
A collection of subsets of a set whose union is not the entire set.
None of the above

What is a relation between two sets?

A set of ordered pairs of elements from the two sets.
A set of unordered pairs of elements from the two sets.
A set of elements that are common to both sets.
None of the above

What is a function between two sets?

A relation between two sets such that each element of the first set is paired with exactly one element of the second set.
A relation between two sets such that each element of the first set is paired with at least one element of the second set.
A relation between two sets such that each element of the second set is paired with exactly one element of the first set.
None of the above

What is the inverse of a function?

A function that undoes the original function.
A function that is the opposite of the original function.
A function that is the same as the original function.
None of the above

What is a bijection between two sets?

A function between two sets that is both one-to-one and onto.
A function between two sets that is one-to-one but not onto.
A function between two sets that is onto but not one-to-one.
None of the above

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