Let A be a set containing n elements. The number of ways of choosing two subsets Pand  Q of  A such that P∩Q=ϕ is

For each x∈A, we have four choices;(i)  x∈P,x∈Q(ii)  x∈P,x∉Q(iii) x∉P,x∈Q(iv) x∉P,x∉QOut of these four choices, last 3 choices imply x∉P∩QThus,  P and  Q can be chosen in 3n ways so thatP∩Q=ϕ