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Questions and Answers
What is a universal set in a given situation?
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?
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?
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?
What is A called if it contains all the elements of set B?
What is a proper subset of a set?
What is a proper subset of a set?
Is set A a subset of set N if A contains only some elements of N?
Is set A a subset of set N if A contains only some elements of N?
What is the difference between a subset and a proper subset?
What is the difference between a subset and a proper subset?
Is set A an equal set to set N if A contains some elements of N?
Is set A an equal set to set N if A contains some elements of N?
What is the notation used to represent a subset?
What is the notation used to represent a subset?
If every element of set C is contained by set D, which of the following statements is true?
If every element of set C is contained by set D, which of the following statements is true?
What is the characteristic of a universal set in a given situation?
What is the characteristic of a universal set in a given situation?
If A is a subset of N, and A contains all the elements of N, then what is the relationship between A and N?
If A is a subset of N, and A contains all the elements of N, then what is the relationship between A and N?
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?
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?
If set A is a proper subset of set N, which of the following statements is true?
If set A is a proper subset of set N, which of the following statements is true?
What is the characteristic of a super set?
What is the characteristic of a super set?
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?
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?
What is the relationship between sets A and B if A is a subset of B, and B is a subset of A?
What is the relationship between sets A and B if A is a subset of B, and B is a subset of A?
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?
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?
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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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