Pipe B:
This is the crankcase breather hose. What happens is some of the air fuel mixture/burnt gases escape past the rings into the crankcase. This is an unavoidible phenomenon as rings never seal a hundred percent. When rings are worn more of these gases make it past into the crankcase.
If left open to the atmosphere these gases can contribute to pollution. Therefore these are led back into the aircleaner to be 'recycled' ie any unburnt gases burnt.
So in your case do attach part B. I suggest using jubilee clips at both the ends to make a good connection and seal.
Of course you will get the jubilee clips AFTER your exams. Dont worry I will give you a long shopping list then!!
For now just attach the pipe B back in place.
Oki dooki??? You wont need to go to the mechanic unless its some REAL issue!!
Best regards (and do post pics as promised after your exams).