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 ≥ 1 i) List the ordered pair of the relation R. ii) Find the domain and range. 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. (3 marks) (1 mark) (2 marks) ii) List in-degrees and out-degrees of all vertices. (3 marks) iii) It is reflexive, symmetric or transitive? Explain the reason of each property. (5 marks) iv) Does R is an equivalence relation? Justify your answer. (1 mark) c) Function f, g and h are given by f(x) = 12-√√x, g(x) = 4/x2 and h(x) = 8x-4 i) Calculate (foh)(5) (2 marks) ii) Calculate (fogoh) (2 marks) iii) Find the inverse of f(x). (2 marks) d) Let R = {-1, 0, 1,2} and S = {-3, -2, -1,6}. For each x ER, define functions p: R-S and q: R→S by: p(x) = x²-2 q(x) = x³-2 Determine if ƒ and g are one-to-one, onto Y, and/or bijection. (4 marks)