mathepi.com

Home   About us   Mathematical Epidemiology   Rweb   EPITools   Statistics Notes   Web Design   Contact us   Links
 
> Home > Statistics Notes > Probability > Union

Union

     If A is a set and B is a set, then we can make a new set from all the elements that are in A or B or both (and nothing else). This new set is written A B. For example, suppose we were going to consider the experiment of tossing a single die. Then the sample space is {1,2,3,4,5,6}. The event of getting one spot is {1}, and the event of getting two is {2}. The event of getting a one or a two is {1} {2} = {1,2}. Or we may consider C={1,2,3}, and D={3,6}. Then C D={1,2,3,6}. The element 3 appears only once; it must be in the union since it appears in at least one of the sets C, D. But there is no definition of an element appearing more than once in a set; all you can say is that an element is in a set or it isn't.
     Notice that A = A no matter what A happens to be. Taking the union of a set A with the empty set just gives you the same set A. Also notice that if we take two sets A and B, then since the union of A and B has all the elements in A as well as those in B, then everything in A has to be in the union of A and B. That union may have some other things in it, but it certainly has everything in A: A A B.
     As another example, we may consider sampling a patient suspected of having tuberculosis disease. A person may have pulmonary disease, or extrapulmonary disease. If L denotes pulmonary disease, and E denotes extrapulmonary disease, then L E denotes the set of people with tuberculosis disease of some kind, whether extrapulmonary, pulmonary, or both.
 
On to intersections.
 

Return to statistics page.
Return to probability page.
Return to stochastic seminar.

All content © 2000 Mathepi.Com (except R and Rweb).
About us.