Introduction to Sets - Universal Set and Subsets

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Questions and Answers

What is a universal set in a given situation?

The set of all the elements being considered from which many other subsets can be formed.

What is denoted by U or {xi} in a set?

The universal set.

What is the relationship between sets A and B if every element of set B is contained by set A?

B is a subset of A.

What is A called if it contains all the elements of set B?

The super set of B. Signup and view all the answers

What is a proper subset of a set?

A subset that contains at least one element less than the set. Signup and view all the answers

Is set A a subset of set N if A contains only some elements of N?

Yes. Signup and view all the answers

What is the difference between a subset and a proper subset?

A subset is any set contained by another set, while a proper subset is a subset that contains at least one element less than the set. Signup and view all the answers

Is set A an equal set to set N if A contains some elements of N?

No. Signup and view all the answers

What is the notation used to represent a subset?

B ⊆ A Signup and view all the answers

If every element of set C is contained by set D, which of the following statements is true?

Set C is a subset of set D. Signup and view all the answers

What is the characteristic of a universal set in a given situation?

It always contains all the elements being considered. Signup and view all the answers

If A is a subset of N, and A contains all the elements of N, then what is the relationship between A and N?

A is an equal set to N. Signup and view all the answers

If set B is a subset of set A, and set B contains all the elements of set A, then what is the notation used to represent the relationship between A and B?

B ⊃ A Signup and view all the answers

If set A is a proper subset of set N, which of the following statements is true?

A contains at least one element less than N. Signup and view all the answers

What is the characteristic of a super set?

It contains all the elements of its subset. Signup and view all the answers

If set A is a subset of set N, and set A contains some elements of set N, then what is the relationship between A and N?

A is a proper subset of N. Signup and view all the answers

What is the relationship between sets A and B if A is a subset of B, and B is a subset of A?

A is an equal set to B. Signup and view all the answers

If set A is a subset of set N, and set A contains all the elements of set N, except one element, then what is the relationship between A and N?

A is a proper subset of N. Signup and view all the answers

Study Notes

Universal Set

A universal set encompasses all elements considered in a specific situation.
Examples include the complete set of students in a school.
Subsets can be formed from the universal set, such as the set of girls, boys, or specific class students.
Denoted by U or represented as {xi}.

Subset and Superset

For sets A = {1, 2, 3, ..., 10} and B = {2, 4, 6, 8, 10}, every element of B is contained in A.
Thus, B is a subset of A, denoted as B ⊆ A.
Conversely, A is a superset of B, denoted as A ⊇ B.

Proper and Improper Subsets

A proper subset is when a set contains at least one fewer element than its superset.
Example: A = {1, 3, 5, 7, 9} is a proper subset of N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Sets A and N are not equal since A has fewer elements, confirming A is a proper subset of N.
An improper subset is when a set is equal to or completely contained in another set.

Application of Subsets

In natural numbers up to 10, A is confirmed as a subset of N but not equal.
The concept of subsets is foundational in set theory, allowing categorization of elements based on shared characteristics.

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Description

Learn about the concept of universal sets, subsets, and super sets in set theory. Understand how to denote and form subsets from a given universal set. Practice your knowledge with this quiz!