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)
Famous quotes containing the words union and/or sets:
“You can no more keep a martini in the refrigerator than you can keep a kiss there. The proper union of gin and vermouth is a great and sudden glory; it is one of the happiest marriages on earth, and one of the shortest-lived.”
—Bernard Devoto (1897–1955)
“Certain anthropologists hold that man, having discovered tools, ceased to evolve biologically. Animals, never having discovered them, continue to fashion drills out of their beaks, oars out of their hind feet, wings out of their forefeet, suits of armor out of their hides, levers out of their horns, saws out of their teeth. Whether this be true or not, all authorities agree that man is the tool-using animal. It sets him off from the rest of the animal kingdom as drastically as does speech.”
—Stuart Chase (1888–1985)