Is the null set a subset of every set? Ever since day one of of my Mathematical Logic course, this fact has really bothered me. I cannot wrap my head around how an empty set is a subset of every possible set. Could someone kindly explain how this is true? Any help is appreciated! 

A remarkably simple way of trying to grasp why that is the case is as follows:

We can consider any set and throw away all its elements, then we are
  left with the subset { }. This means that { } is a subset of any set.

