I have 2 proofs i can't seem to get

one is prove by induction the power set

abs(P(A))=2^n where abs(A)=n

I think you need to use a binomial theorem of sorts to solve this one

another one that is giving me trouble is

3 divides n if and only if 3 divides the sum of the digits of n, where n is a positive integer

this one is also an induction proof thanks for any help