2. (22 points) Given the following directed graph showing a relation R of flights between cities. Answer the following questions MX MSP MQT DTW ORD (a) (1pt) Give the set A the relation R is on (b) (lpt) 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 (list all ordered pairs explicitly) (e) (2pt) Find the reflexive closure of R (list all ordered pairs explicitly) (f) (2pt) Find R-1 (list all ordered pairs explicitly). (g) (2pt) Find the symmetric closure of R. (h) (1pt) Describe what the pairs in Ro R represent (i) (2pt) Find Ro R (list all ordered pairs explicitly) (Gi) (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 all ordered pairs explicitly)