Relationships Between Sets Union If we have two sets we might want to combine them into one big set. The Union of A and B is written We dont bother to write the duplicate(s) twice. A = {1, 2, 3} and B = {3, 4, 5} Union Its just like real life! Two people get married (union) and merge their CD collections Union They sell all the duplicates on eBay. The CDs that are left are the union of their collections. all of hers + all of his dups Union Mathematically, we say that the number of elements in the union of two finite sets is: the number of elements in Set A (his DVDs) PLUS the number of elements in Set B (her DVDs) MINUS the number of elements in the intersection of the sets (duplicates). The DVDs that are left are the union of their collections. all of hers + all of his dups Intersection Just like the intersection of two roads, the intersection of two sets are the elements that are members of both sets. Intersection Set A = { 1, 2, 3 } set B = { 3, 4, 5 } The empty set Set A = { 1, 2, 3 } set B = { 4, 5, 6 } There is no element that is in both sets, so the intersection is the empty set. The empty set The symbol for the empty set is the Greek letter Phi Do not put it in brackets. is not empty. It is a set with one element the Greek letter Phi Venn Diagrams One way to graphically represent sets is by using Venn diagrams. John Venn (1834 1923), was a British logician and philosopher who introduced the Venn diagram, which is used in many fields, including set theory, probability, logic, statistics, and computer science. Courtesy of Wikipedia Universal Set To use a Venn diagram, you must first start with a universal set, represented by U, which contains all of the elements being considered in a problem. U = {all the puppies in a litter} Universal Set In a problem about Chevys and Fords, the universal set could be the set of all cars or it could be the set of all trucks it just has to include all of the vehicles that youre going to be talking about. Venn Diagram If U = {all cars} and F = {all Ford cars}, the Venn diagram would look like this: Its easy to see that F is a proper subset of U. U F Venn Diagram The complement of F is the set that consists of all of the members of U that are not in F The complement of F is written F. The complement would be all cars that are NOT Fords. U F (the blue area) Venn Diagram If U = {all cars}, and F = {all Ford cars}, and C = {all Chevy cars} the Venn diagram would look like this: Its easy to see that both F and C are subsets of U. U F C Disjoint Sets In this case, the sets are disjoint - meaning that they dont overlap. U FC There are no cars that are both Fords and Chevys - my neighbor sort of has one, but thats a long story Intersection R = {redheads} G = {people with green eyes} Venn diagrams make it easier to see how sets relate. Vocabulary Union Intersection Empty set Venn Diagram