Expert: Scott A Wilson - 10/16/2009

Question
Hi

could you plz give me a hint about the problem below:

Use induction on the size of S to show that if S is a finite set , then |2^S| = 2^|S|.

actually i can't understand if S is a set like S = {a , b} , how can we define something like 2^S for it and what does 2^S indicates?

thanx
Bita

Answer
Take S as (2,3,4).  |S| = √(2²+3²+4²) = √(4+9+16) = √29.

S^2 = 29, so |S^2| = 29.
|S|^2 = |S||S| = √29√29 = 29.

I believe that somehow a typo was found, since I don't understand 2^S.
I believe it was suppose to b e S^2.