ABCD
ABE
ABC
EF

Using the "store everything in the powerset approach" (or, at least allocating space for it), we need to store 2^6 elements (A,B,C,D,E,F) or 64 bytes of data. We're going to assume that we know in advance that there are only 6 possible elements.

For sake of argument, let's assume a more compact efficient approach along the lines of the original approaches using hash tables. We'd build up a structure like this, in some arbitrary order:

#first set
ABCD
BCD
ACD
ABD
ABC
AB
AC
BC
AD
BD
CD
A
B
C
D
#second set
ABE
AE
BE
E
#third set
#generates nothing
#fourth set
EF
F

This only requires 22 bytes of data, a 65% memory savings.