If the power set PS S what is SSolutionGiven that PS S The

If the power set P(S) = S, what is S?

Solution

Given that

P(S) = S

The power set of any set S, written P(S), is the set of all subsets of S, including the empty set and S itself.

S = Set as a collection of its elements if the elemement be sets themselves

Example:

  If S is the set {x, y, z }, then the subsets of S are:

S = 2ⁿ ,n = number of elements in S

   Here,

   n = 3

S = 2³ = 8

S = { {} , {x} , {y} , {z} , {x,y} , {y,z} , {x,z} , {x,y,z} }

Hence,

P(S) = { {} , {x} , {y} , {z} , {x,y} , {y,z} , {x,z} , {x,y,z} }