This assignment will assess your skills and knowledge about: Discussing properties of reflexivity, symmetry, and transitivity relation to solve real world problems. Assignment: Scenario: A university wants to analyze student enrollments to form study groups. A relation R is defined on a set of students S = {a, b, c, d, e}, such that "xRy if and only if students x and y are enrolled in at least two common courses." The course enrollments for each student are as follows: Student 'a' is enrolled in Math, Physics, and CS Student 'b' is enrolled in Math, CS, and English Student 'c' is enrolled in Physics and Chemistry Student 'd' is enrolled in Math and CS Student 'e' is enrolled in Physics and English Using the given scenario, respond to the following discussion prompts: Determine the set of pairs (x, y) that satisfy the given relation R i.e. find R = {(x, y) | x, y S and xRy}. If the university wants to form study groups such that each group consists only of students who are equivalently related, how many groups should be formed and list all groups explicitly? Discuss the difference between a partial order relation and an equivalence