■ To verify that two sets A and B are equal, written A = B, show that for every x, if x ∈ A, then x ∈ B, and if x ∈ B, then x ∈ A.
■ To verify that two sets A and B are not equal, written A ≠ B, find at least one element that is in A but not in B, or find at least one element that is in B but not in A. One or the other conditions sufces; you need not (and may not be able to) show both conditions.
■ To verify that A is a subset of B, written A ⊆ B, show that for every x, if x ∈ A,