How do you prove that the null set is a subset of all sets?No.

The null set is an empty set, and includes nothing within
the brackets.  Every set that has at least one element, has a subset that is lacking any
elements, also known as the null set. 

Let's look at the
set of numbers that includes 1, 2, & 3.

It would be
written {1,2,3}

subsets would be {1,2}, {1,3}, {2,3}, {1},
{2}, {3}, and {}. 

Let's look at this from a completely
different perspective.  You have a fresh baked apple pie.  The pie (set) is divided up
(subsets) and eaten.  You are left with an empty pie plate.  The pie plate represent the
brackets and the emptiness is your nul set. 

I hope this
helps explain.