1. What Is the Union of Sets?
The union of sets collects all elements that appear in either of the sets or in both. It simply brings the sets together without repeating any element.
This operation is useful when combining information from multiple sets.
2. Notation
The symbol for union is:
\( A \cup B \)
This is read as “A union B”.
3. Meaning of A ∪ B
\( A \cup B \) contains:
- All elements in A
- All elements in B
- Each element only once
4. Examples
Here are simple examples to understand the union clearly:
4.1. Example 1
\( A = \{1,2,3\}, B = \{3,4,5\} \Rightarrow A \cup B = \{1,2,3,4,5\} \)
4.2. Example 2
\( X = \{a,b\}, Y = \{b,c,d\} \Rightarrow X \cup Y = \{a,b,c,d\} \)
4.3. Example 3
Union removes repetition automatically:
\( \{1,1,2\} \cup \{2,3\} = \{1,2,3\} \)
5. Union of More Than Two Sets
Union can be extended to three or more sets in the same way.
5.1. Example
If A = {1,2}, B = {2,3}, C = {3,4}, then:
\( A \cup B \cup C = \{1,2,3,4\} \)
6. Union in Venn Diagrams
In a Venn diagram, the union of sets is shown by shading both circles, including the overlapping part.
7. Important Points
A few things to remember about union:
7.1. Key Ideas
- The union includes every element from both sets.
- Duplicate elements appear only once.
- Union works for any number of sets.
- Order does not matter: \( A \cup B = B \cup A \).