Students should have already seen at least most of the basic set identities proven in at least one way. Now students will use those basic set identities to prove other set identities algebraically. Here are a couple examples of identities which can be proven in this way:

$$\begin{align} & (A \cap B) \cup \left(A \cap B^\complement\right) = A \\[0.5em] & (A - C) \cap (C - B) = \emptyset \end{align}$$