Solve the following problems and show your work:

(f) Suppose A is a finite set with n elements. How many relations Ull (4. (a) Let A = (a, b, c] and R = [(a, b), (b, b), (b, c), (a, c). (b, a) ). Is R a transitive relation? (b) Which of the following relations on R are reflexive? Which are symmetr Which are transitive? (i) x Ry if x - y is rational. (ii) x Ry if x - y is irrational. (iin) x Ry if lx - yl