Okay, but Joshua Bloch's elegant Collections Framework
gives you all the set operations--and they work between different
Set implementations (including EnumSet) very conveniently.
EnumSet implements the Collections Framework's root
interface, Collection, and, of course, its subinterface, Set.
It turns out that EnumSet's relevant bulk operations are
way up in the Collection interface, and they are defined
explicitly as set operations in the API for the Set interface.
(Are interfaces neat or what?)

Bloch's excellent tutorial on the Java Collections Framework
is at

http://java.sun.com/docs/books/tutorial/collections/

The following is from the tutorial

The bulk operations are particularly well suited to Sets; when applied to
sets, they perform standard set-algebraic operations. Suppose s1 and s2 are
Sets. Here's what the bulk operations do:
 a.. s1.containsAll(s2): Returns true if s2 is a subset of s1. (s2 is a
subset of s1 if set s1 contains all the elements in s2.)
 b.. s1.addAll(s2): Transforms s1 into the union of s1 and s2. (The union
of two sets is the set containing all the elements contained in either set.)
 c.. s1.retainAll(s2): Transforms s1 into the intersection of s1 and s2.
(The intersection of two sets is the set containing only the elements that
are common to both sets.)
 d.. s1.removeAll(s2): Transforms s1 into the (asymmetric) set difference
of s1 and s2. (For example, the set difference of s1 - s2 is the set
containing all the elements found in s1 but not in s2.)

Fooling around directly with bits is a heck of a lot of dithering compared
with the way Bloch specified and implemented set operations in the
Java Collections Framework--and you still get the efficiency of bit
vector dithering, because the implementation of EnumSet uses bit
vectors behind the high level scene.

George W. Cherry