University of California, San Diego: Edward Bender and S. Williamson's "Sets, Equivalence and Order: Sets and Functions"

Study Theorem 1 on pages SF-2 and SF-3 on the distributive laws: A \cap  (B \cup  C) = (A \cap  B) \cup  (A \cap  C); A \cup  (B \cap  C) = (A \cup  B) \cap  (A \cup  C). The former shows union distributes over intersection; and the latter shows intersection distributes over union. Prove the distributive laws. 
Click https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2011/09/CS202-Sets-and-Functions-Edward-Benderand-S.-Gill-Williamson.pdf link to open resource.