Example of Equal Sets
Let P be the set of all integers greater than 0 and Q be the set of all natural numbers.
Then, P = {1, 2, 3, 4,…..} and Q = {1, 2, 3, 4,….}.
As we can see, all elements of P are the same as all the elements of Q, P and Q are equal sets.
Some other examples include:
- A = { 1, 2, 3, 4, 5} and B = {2, 3, 1, 5, 4}.
- Set of alphabets in words “listen” and “silent”.
- Set of fractions {1/2, 2/4, 3/6} and {6/12, 4/8, 2/4}.
Equal and Unequal Sets
The key differences between both equal and unequal sets are as follows:
Aspect | Equal Sets | Unequal Sets |
---|---|---|
Definition | Two sets have the same elements. | Two sets have different elements. |
Notation | A = B | A ≠ B |
Cardinality | Equal | May or Maynot be Equal |
Examples | {1, 2, 3} = {3, 2, 1} | {1, 2, 3} ≠ {4, 5, 6} |
Subsets | Every subset of A is also a subset of B, and vice versa. | Subsets may differ. |
Intersection | A ∩ B = A (or B) | A ∩ B has common elements of both A and B. |
Union | A ∪ B = A (or B) | A ∪ B combines elements of both A and B. |
Complement | Complement of A is same as complement of B. | Complements of unequal sets differs. |
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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