For all sets A and B, A^c ∪ B^c ⊆ (A ∪ B)^c.

The following is a proposed proof for the statement.

1) Suppose A and B are any sets, such that x ∈ A^c ∪ B^c.

2) Then x ∈ A^c or x ∈ B^c by definition of union.

3) It follows that x ∉ A or x ∉ B by definition of complement, and so x ∉ A ∪ B by definition of union.

4)Thus x ∈ (A ∪ B)^c by definition of complement, and hence A^c ∪ B^c ⊆ (A ∪ B)^c by definition of subset.

Identify the error(s) in the proposed proof. (Select all that apply.)

A) It is possible for x ∈ A^c ∪ B^c to be true and x ∈ A^c or x ∈ B^c to be false.

B) It is possible for x ∉ A or x ∉ B to be true and x ∉ A ∪ B to be false.

C) The proof does not handle the case when B ⊆ A.

D) The proof assumes what is to be proved.

E) The proof does not handle the case when A ⊆ B.