2. (22 points) Given the following directed graph showing a relation R of flights between cities. Answer the following questions. (a) (1pt) Give the set A the relation R is on. (b) (1pt) Give the relation R (that is, list the ordered pairs explicitly) (c) (2pt) Express the relation R as a zero-one matrix (present cities in alphabetic order, e.g., CMX, DTW, MQT, ..) (d) (2pt) Find the diagonal relation on A st al ordered pairs explicitly) (e) (2pt) Find the reflexive closure of R (stl ordered pairs explicitly) (f) (2pt) Find R-1 (list all ordered pairs explicitly) (g) (2pt) Find the symmetric closure of IR (h) (1pt) Describe what the pairs in Ro R represent (i) (2pt) Find RoR (list all ordered pairs explicitly) ) (1pt) Describe what the pairs in R3 represent (k) (2pt) Find R3 (list all ordered pairs explicitly) (1) (1pt) Describe what the transitive closure, R' represents. (m) (3pt) Find R (list al ordered pairs explicitly)