Consider your eight-digit student ID as a set of single-digit integers. For example, if your student ID is the number 01238586, then it represents the set S = {0, 1, 2, 3, 5, 6, 8}. Now consider your student ID as a sequence of eight digits. For example, if your student ID is the number 01238586, then it represents the sequence D = (0, 1, 2, 3, 8, 5, 8, 6). The sequence can be used to define a relation r:S →→→→S by creating the elements of r as follows, = {(d₁, d₂), (d3, d₁), (d5, d6), (d7, ds)} The di, 1 ≤ i ≤ 8 are the digits in the sequence read left to right. For example, if your student ID is the number 01238586, then r = {(0, 1), (2, 3), (8,5), (8,6)} Questions to Answer a. Create the relation r using your student ID. Record the relation in roster notation as a set of 2- tuples (see example). b. Extend your relation by adding the 2-tuple (d₂, d₁) to r, creating the relation R. That is, R=rU {(d₂, d₁)} Record the relation R as a set of 2-tuples c. Find the transitive closure, T, of the relation R. Record the relation T as a set of 2-tuples.