For any set A, finite or infinite, let B^A be the set of all functions mapping A into the set B = {0, 1 }. Show that the cardinality of B^A is the same as the cardinality of the set P(A). Then try to prove your conjecture.

For any set A, we denote by P(A) the collection of all subsets of A. For example, if A = {a, b, c, d}, then {a, b, d} ∈ P(A). The set P(A) is the power set of A.