Let E be a set, A and B two subsets ofE. We consider the following map f: f:P(E) -> P(A) x P(B), x -> (x ∩ A, x ∩B). Justify that f is well defined. Suppose that A ∪ B = E and...

Which of the following statements correctly justifies that the map f is well defined?

Options:
A. Let E be a set, A and B two subsets ofE. We consider the map f: f:P(E) -> P(A) x P(B), x -> (x ∩ A, x ∩B). Justify that f is well defined.
B. Suppose that A ∪ B = E and let x be an element of P(E). Then, f(x) = (x ∩ A, x ∩B). This shows that f is well defined.
C. The map f is well defined because A and B are subsets of E and the map f assigns each element x of P(E) to a unique pair (x ∩ A, x ∩B).
D. The map f is well defined because the intersection of any set x with subsets A and B will always result in a valid pair (x ∩ A, x ∩B).