Question 2 Suppose there is a set of growers G = {a, b, c, d}, a set of retailers R = {e, f, g} and a set of customers C = {m, n, p, q, r}.

Question 2

Suppose there is a set of growers G = {a, b, c, d}, a set of retailers R = {e, f, g} and a set of customers

C = {m, n, p, q, r}. There are two relations A and B on G ´ R and R ´ C, respectively, defined by:

aAe, bAg, cAf, dAe, dAg, and eBn, eBr, fBm, fBq, gBp

xAy means "grower x sold goods to retailer y", and

yA-1x means "retailer y bought goods from grower x"

xBy means "retailer x sold goods to customer y", and

yB-1x means "customer y bought goods from retailer x"

(i)             Find the matrices M(A) and M(B) that represent the relations A and B.

(ii)           Find the matrices M(A)T and M(B)T that represent the relations A-1 and B-1

(iii)          Consider the query:

Which customers have received goods that came from

the same grower(s) as those goods received by customer p?

Find the logical matrix products M(A) M(B) and then M(B)T M(A)T, and finally M(B)T M(A)T M(A) M(B), and hence answer the query.