Union of Two Sets
The union of two sets A and B is the collection of points which are in A or in B or in both A and B. In symbols,
- .
For example, if A = {1, 3, 5, 7} and B = {1, 2, 4, 6} then A ∪ B = {1, 2, 3, 4, 5, 6, 7}. A more elaborate example (involving two infinite sets) is:
- A = {x is an even integer larger than 1}
- B = {x is an odd integer larger than 1}
If we are then to refer to a single element by the variable "x", then we can say that x is a member of the union if it is an element present in set A or in set B, or both.
Sets cannot have duplicate elements, so the union of the sets {1, 2, 3} and {2, 3, 4} is {1, 2, 3, 4}. Multiple occurrences of identical elements have no effect on the cardinality of a set or its contents. The number 9 is not contained in the union of the set of prime numbers {2, 3, 5, 7, 11, …} and the set of even numbers {2, 4, 6, 8, 10, …}, because 9 is neither prime nor even.
Read more about this topic: Union (set Theory)
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—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)