Правильный способ TDD-методов, который вызывает другие методы

I need some help with some TDD concepts. Say I have the following code

def execute(command)
  case command
  when "c"
    create_new_character
  when "i"
    display_inventory
  end
end

def create_new_character
  # do stuff to create new character
end

def display_inventory
  # do stuff to display inventory
end

Now I'm not sure what to write my unit tests for. If I write unit tests for the execute method doesn't that pretty much cover my tests for create_new_character and display_inventory? Or am I testing the wrong stuff at that point? Should my test for the execute method only test that execution is passed off to the correct methods and stop there? Then should I write more unit tests that specifically test create_new_character and display_inventory?