QUESTION 3 (25 MARKS a) Let A = {2, 4, 6) and B = {2, 3, 5, 8, 10) and R be the relation from A to B defined by aRb if and only if 2b - 3a 21 i) List the ordered pair of the relation R. (3 marks) ii) Find the domain and range. (1 mark) b) Let R = {(2,2), (2,9),(5,5),(5,9), (6,2), (6,5), (6,6), (9,6), (9,9)} from X = {2,5, 6,9) i) Show the matrix for the relation R. ii) List in-degrees and out-degrees of all vertices. iii) It is reflexive, symmetric or transitive? Explain the reason of each property. iv) Does R is an equivalence relation? Justify your answer. (2 marks) (3 marks) (5 marks) (1 mark) c) Function f g and h are given by f(x) = 12 - Vx, g(x) = 4/x2 and h(x) = 8x - 4 i) Calculate (foh)(5) ii) Calculate (f.goh) iii) Find the inverse of f(x). (2 marks) (2 marks) (2 marks) d) Let R = (-1,0,1,2) and S = (-3, -2,-1,6}. For each x € R, define functions p: R-S and q: R-S by: p(x) = -x-2 9(x) = x3 - 2 Determine iff and g are one-to-one, onto Y, and/or bijection. (4 marks)