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 of, union and/or sets:
“Those graceful acts,
Those thousand decencies, that daily flow
From all her words and actions, mixed with love
And sweet compliance, which declare unfeigned
Union of mind, or in us both one soul.”
—John Milton (1608–1674)
“Some are petitioning the State to dissolve the Union, to disregard the requisitions of the President. Why do they not dissolve it themselves,—the union between themselves and the State,—and refuse to pay their quota into its treasury? Do not they stand in the same relation to the State that the State does to the Union? And have not the same reasons prevented the State from resisting the Union which have prevented them from resisting the State?”
—Henry David Thoreau (1817–1862)
“There be some sports are painful, and their labor
Delight in them sets off. Some kinds of baseness
Are nobly undergone, and most poor matters
Point to rich ends.”
—William Shakespeare (1564–1616)