@Alejandro Jakubi Thank you for the suggestion. 

It does what I want partially (i.e. just what I asked in my question! :)) - I want the results to be also sets that I can do further analysis on. This is what is happening right now:

s1 := {0 < x, x < 100};
s2 := {5 < x, x < 95};
a1 := MathematicalFunctions:-`&Minus`(s1, s2);
    Or(And(95 <= x, x < 100), And(x <= 5, 0 < x))
a2 := MathematicalFunctions:-`&Union`(s1, s2);
    And(0 < x, x < 100)
type(s1, set);
   true
type(s2, set);
   true
type(a1, set);
   false
type(a2, set);
   false

1. How do I make the results also sets?

2. How do we find out about these undocumented features?!