Problem 3 N-ary Relation

a. A set is defined as A B C where A { 1, 2, 3,4}; B = {1, 5, 6}; C = {2, 3}. Which of the following subsets are relations of A B C? Explain your answer

(i) {(1, 1, 2), (2, 5, 3), (2, 2, 2}, (4, 6, 3)}

(ii) {(1, 5, 3), (1, 4, 2), (4, 5, 4)}

b. Given the three sets A = {Kim, Tom, John}, B = {biology-major, arts-major, CS-major}, C = {$40K, $20K, $70k}, {biology-major, arts-major, CS-major}, show that the following subset is a relation of the Cartesian product A B C, and show the relation in tabular form. {(Kim, CS-major, $70K), (Tom, arts-major, $20K), (John, biology-major, $40K)}

c. For the table derived in problem 3B, give the projections P({1, 3}) in a tabular form

d. Given the relation given below for the sets in problem, 3b, which key can act as primary key and why?. Explain. {(Kim, CS-major, $70K), (Tom, CS-major, $70 K), (john, biology-major,$40k)}