Is a void set a proper or improper subset of any non void set ?

Given a set A , a proper subset is any set B such that B ⊆ A and B ≠ A ; that is, B is contained in A but is not equal to A . This is denoted by B ⊂ A in some texts. So while A is a subset of itself, it is not a proper subset of itself. And this is true for any set, even the empty set (or void set, as you call it).