Properties of Equal Sets
There are various properties of equal sets, some of which are listed as follows:
- The intersection of two equal sets is equal to both sets, i.e., if A = B then, A ∩ B = A = B.
- Two equal sets are always subsets of each other, i.e., if A ⊂ B and B ⊂ A, then A = B.
- For two sets to be equal, the order of their elements does not matter, i.e., {9, 10, 11} = {11, 10, 9}.
- The cardinality of equal sets and their power set are the same.
- Equal sets always have the same number of elements.
- The elements of two equal sets are equal.
Related Article,
Equal Sets: Definition, Cardinality, and Venn Diagram
Equal Set is the relation between two sets that tells us about the equality of two sets i.e., all the elements of both sets are the same and both sets have the same number of elements as well. As we know, a set is a well-defined collection of objects where no two objects can be the same, and sets can be empty, singleton, finite, or infinite based on the number of its elements.
Other than that, there can be sets based on the relationships between two sets such as subsets, equivalent sets, equal sets, or it can set of subsets for any set, i.e., power sets, etc. This article explores one such relationship of sets known as Equal Set, including definition, examples, properties as well as Venn diagram.
Table of Content
- What are Equal Sets?
- Equal Sets Definition
- Equal Set Symbol
- Example of Equal Sets
- Equal and Equivalent Sets
- Venn Diagram of Equal Sets
- Properties of Equal Sets
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