How does one prove that A intersecting B = A, iff A is a subset of B? Suppose A and B are subsets of U. How do you show that below, if any one of the relations stated holds, then each of the others holds: A ⊆ B, U ∖ A ⊇ U ∖ B, A ∪ B = B, A ∩ B = A?