What is the maximum number of different Boolean functions involving n Boolean variables?

Answer 1

A Boolean function f is a function that maps Bk->B where B ={0,1} and k is a nonnegative integer. The term "arity" of the function is denoted by k. Fo every k there are 22k k-ary functions for each k. given n input variables, there are 2n bits in function's number. Now given m bits, there are 2m different values. So, for n input variables there are m=2n possible bits and 2m or 22n possible functions.