2. Suppose that |S| = n. Use induction to prove |2^S| = 2^|S|. 2^S is the notation for the power set of S.

(Please don't use other peoples answers for this question. I am confused on how to add |2^k| + (k+1) when we are adding k+1 to both sides of the equation in P(k) to prove that P(k+1) is true under the assumption that P(k) is true.) There is the sets in the book called Discrete mathematics and its applications by Rosen Kenneth.) Thank you in advance!