Both definitions are from Syntax; A generative introduction (4th edit.)
c-command: Node A c-commands node B if every 'branching' node dominating A also dominates B, and neither A nor B dominate the other.
Q1) What would be wrong or different if we assume that definition of c-command does not include 'branching'?
government: Node A governs node B if A c-commands B and there is no node G such that G is c-commanded by A and G asymmetrically c-commands B.
Q2) What would be wrong or different if we assume that definition of goverment does not include 'G asymmetrically c-commands B'?
Can you explain with some of samples? Thanks!!!