Question

how many element does set A contains if it has 64 subset and 255 proper subsetdas

Answer 1

since 64 is 2^6

and since a set of n elements has 2^n subsets, from
set A contains 64 subset, I would say it has 6 elements.

Don't know what you mean by "255 proper subsetdas" .

Answer 2

256 = 2^8

a set of N elements has 2^N subsets, of which one is empty.