1.6 Algebra of Sets and De Morgan's Laws

Using Distributive Law in reverse: $(A \cup B) \cap (A \cup B')$ $= A \cup (B \cap B') \quad (\text{Extracting common A})$ $= A \cup \phi \quad (\text{Complement law})$ $= A$

Alternative method (Venn): $A \cup B$ is everything in A or B. $A \cup B'$ is everything in A or outside B. The intersection is just A.