Question 4 (11 marks) (a) Let ab € Z. Let R be a relation on the set of positive integers such that a Rb if 6 divides (a

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Question 4 11 Marks A Let Ab Z Let R Be A Relation On The Set Of Positive Integers Such That A Rb If 6 Divides A 1 (31.78 KiB) Viewed 19 times

Question 4 (11 marks) (a) Let ab € Z. Let R be a relation on the set of positive integers such that a Rb if 6 divides (a - b). Show that Ris an equivalence relation. (4 marks) (b) Let A = {1, 2, 3, 4, 5). The following relations are on A. Find R2 R1 if: Ri= {(1,1),(1,2), (2,1), (2,3), (3,2), (3,5)} R2 = {(1,2), (1, 3), (2,4) (3,4), (3,5), (5,3)} [2 marks] () Let R1 and R2 be relations on A = {1, 2, 3, ..,4} such that R1 = {(a, b) as b}and R2 = {(a, b)|a+b<5). List the elements of R1 and R2 and represent them as matrices (with the elements of this set listed in increasing order). [3 marks] (d) Display the table produced by applying the projection P1.45 to Table 1 below. First name Last name Major GPA Year Level Tel. Number 611-2342 611-7835 Andrea Matthew Matt Jose 2.45 3.99 1 2 Biology Computer Science Math Math Alex Arthur Alexanzer Moon 549-0023 349-9023 3.57 4.12 2 3 [2 marks]