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 DeMorgan's laws: (A \cup  B) ' = A' \cap B'; (A \cap  B)' = A' \cup B'. In English, the complement of A union B is the intersection of A complement and B complement; and the complement of A intersect B is the complement of A union the complement of B. DeMorgan's laws are famous and appear in many places in mathematics, engineering, and computer science. Prove DeMorgan's Laws.
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