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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 x R and R x 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 *x means "retailer y bought goods from grower x"
xBy means "retailer x sold goods to customery", and yB"
*x 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) and M(B) that represent the relations A" and B"
(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) ' M(A) , and finally
M(B)' M(A) M(A) M(B), and hence answer the query.
[ Hint: To see a similar exercise, look at the "Application" on page 13 of Lecture 5.]
[1 + 1 + 3 = 5 marks

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