Prove the following about the dom relation: a) If a dom b and b dom c, then a dom c (transitivity). b) It is never possible that both a dom b and b dom a hold, if a ^ b (antisymmetry) .  c) If a and b...

Prove the following about the dom relation:


a) If a dom b and b dom c, then a dom c (transitivity).


b) It is never possible that both a dom b and b dom a hold, if a ^ b (antisymmetry) .

c) If a and b are two dominators of n, then either a dom b or b dom a must hold.


d) Each node n except the entry has a unique immediate dominator — the dominator that appears closest to n along any acyclic path from the entry to n.