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Equal Sets: Difference between revisions

Created page with "= Equal Sets - Definition and Examples= In set theory, '''equal sets''' are sets that contain the '''exact same elements'''. The order of elements or how they are written does not matter, only the content does. == Definition of Equal Sets == Two sets A and B are said to be '''equal''' if they have '''exactly the same elements'''. This means every element of set A is in set B, and every element of set B is in set A. * Mathematically: <math>A = B \iff (x \in A \Rightar..."
 
 
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=== Example 3: ===
=== Example 3: ===
Let <math>E = \{\text{vowels in "APPLE"}\} = \{A, P, L, E\}</math>   
Let E be the set of vowels in the word "APPLE". 
<math>F = \{A, E, L, P\}</math>
The vowels are: A and E (note: repeated letters are not included more than once).
Then '''E = F''' because they contain the same distinct letters.
 
<math>E = \{A, E\}</math>
 
Let F be another set:  
<math>F = \{E, A\}</math>
 
Then '''E = F''' because both sets have the same elements, even though the order is different.


== How to Verify if Sets are Equal ==
== How to Verify if Sets are Equal ==
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