Editing Associative Law of Sets (section)

== Associative Law for Union ==

For any three sets <math>A</math>, <math>B</math>, and <math>C</math>:

<math>
(A \cup B) \cup C = A \cup (B \cup C)
</math>

This means that whether you first unite <math>A</math> and <math>B</math> and then unite the result with <math>C</math>, or first unite <math>B</math> and <math>C</math> and then unite the result with <math>A</math>, the final set is the same.

=== Example: Union ===  
Let  
<math>A = \{1, 2\}</math>  
<math>B = \{2, 3\}</math>  
<math>C = \{3, 4\}</math>  

Calculate <math>(A \cup B) \cup C</math>:

<math>A \cup B = \{1, 2, 3\}</math>  
<math>(A \cup B) \cup C = \{1, 2, 3\} \cup \{3, 4\} = \{1, 2, 3, 4\}</math>

Calculate <math>A \cup (B \cup C)</math>:

<math>B \cup C = \{2, 3, 4\}</math>  
<math>A \cup (B \cup C) = \{1, 2\} \cup \{2, 3, 4\} = \{1, 2, 3, 4\}</math>

Both are equal:

<math>(A \cup B) \cup C = A \cup (B \cup C) = \{1, 2, 3, 4\}</math>