Given Ƥ, the power set function, and Ø, the empty set,what are Ƥ(Ø), Ƥ(Ƥ(Ø)) and Ƥ(Ƥ(Ƥ(Ø))) ?
How many members are there in Ƥ4(Ø) and Ƥ5(Ø) ?

Answers:
Ƥ1(Ø) = {Ø}                     cardinality: 20 = 1
Ƥ2(Ø) = {Ø,{Ø}}                 cardinality: 21 = 2
Ƥ3(Ø) = {Ø,{Ø},{{Ø}},{Ø,{Ø}}}   cardinality: 22 = 4
Ƥ4(Ø) = {
          Ø,
          {Ø},
          {{Ø}},
          {{{Ø}}},
          {Ø,{Ø}},
          {Ø,{{Ø}}},
          {{Ø,{Ø}}},
          {{Ø},{{Ø}}},
          {Ø,{Ø,{Ø}}},
          {Ø,{Ø},{{Ø}}},
          {{Ø},{Ø,{Ø}}},
          {{{Ø}},{Ø,{Ø}}},
          {Ø,{Ø},{Ø,{Ø}}},
          {Ø,{{Ø}},{Ø,{Ø}}},
          {{Ø},{{Ø}},{Ø,{Ø}}},
          {Ø,{Ø},{{Ø}},{Ø,{Ø}}}
        }                       cardinality: 24 = 16

There are 216 members in Ƥ5(Ø)

# posted by rot13(Unafba Pune) @ 9:05 PM