A is a set containing n  elements. A subsetP of A  is chosen. The set A  is reconstructed by replacing the elements of P.  A  subset Q  of A is again chosen. The number of ways of choosing P  and  Q  so that P∩Q=ϕ  is

Let A={a1, a2, ......., an}.  For ai∈A  , we have the following choices     (i)          ai∈P  and  ai∈Q                             (ii)        ai∈P  and  ai∉Q    (iii)       ai∉P  and  ai∈Q                              (iv)      ai∉P  and  ai∉Q Out of these only (ii),(iii) and (iv) imply ai∉P∩Q. Therefore, the number of required subsets is 3n.