If A = {a, b, c},

The collection of all subsets of a set A is called the power set of A. It is denoted by P(A).

Now, We know that ϕ is a subset of every set. So, ϕ is a subset of {a, b, c}.

Also, {a},{b},{c},{a,b},{b,c},{a,c} are also subsets of {a, b, c}

We know that every set is a subset of itself. So, {a, b, c} is a subset of {a, b, c}.

Thus, the set {a, b, c} has, in all eight subsets, viz. ϕ , {a},{b},{c},{a,b},{b,c},{a,c},{a, b, c}.

∴ P(A) = { ϕ , {a},{b},{c},{a,b},{b,c},{a,c},{a, b, c}}

Now, n{P(A)} = 2^m , where m = n(A) = 3

⇒ n{P(A)} = 2³ = 8