Suppose that A is the multiset that has as its elements the types of computer equipment ne...

Suppose that A is the multiset that has as its elements the types of computer equipment needed by one department of a university and the multiplicities arc the number of pieces of each type needed, and B is the analogous multiset for a second department of the university. For instance. A could be the multiset {107 personal computers. 44 routers. 6 servers} and B could be the multiset {14 personal computers. 6 routers. 2 mainframes),

a) What combination of A and B represents the equipment the university should buy assuming both departments use the same equipment?

b) What combination of A and B represents the equipment that will be used by both departments if both departments use the same equipment?

c) What combination of A and B represents the equipment that the second department uses, but the first department does not. if both departments use the same equipment?

d) What combination of A and B represents the equipment that the university should purchase if the departments do not share equipment?

Fuzzy sets are used in artificial intelligence. Each element in the universal set U has a degree of membership, which is a real number between 0 and 1 (including 0 and 1), in a fuzzy set S. The fuzzy set S is denoted by listing the elements with their degrees of membership (elements with 0 degree of membership are not listed). For instance, we write (0.6 Alice, 0.9 Brian. 0.4 Fred. 0.1 Oscar, 0.5 Rita) for the set F (of famous people) to indicate that Alice has a 0.6 degree of membership in F, Brian has a 0.9 degree of membership in F, Fred has a 0.4 degree of membership in F, Oscar has a 0.1 degree of membership in F. and Rita has a 0.5 degree of membership in F (so that Brian is the most famous and Oscar is the least famous of these people). Also suppose that R is the set of rich people with R = {0.4 Alice. 0.8 Brian. 0.2 Fred. 0.9 Oscar, 0.7 Rita).