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:
“My Christian friends, in bonds of love, whose hearts in sweetest union join,
Your friendship’s like a drawing band, yet we must take the parting hand.
Your company’s sweet, your union dear; Your words delightful to my ear,
Yet when I see that we must part, You draw like cords around my heart.”
—John Blain (18th century)
“To me this world is all one continued vision of fancy or imagination, and I feel flattered when I am told so. What is it sets Homer, Virgil and Milton in so high a rank of art? Why is Bible more entertaining and instructive than any other book? Is it not because they are addressed to the imagination, which is spiritual sensation, and but mediately to the understanding or reason?”
—William Blake (1757–1827)